@inproceedings{Geiger_HoferTemmel__GraphBasedLosslessMarkovLumpings__ISIT_2016,
 author = {Geiger, Bernhard C.
       and Hofer-Temmel, Christoph
       },
 title = {Graph-Based Lossless Markov Lumpings},
 booktitle = {Proc. IEEE Int. Sym. on Information Theory (ISIT)},
 language = {English},

 year = {2016},

 abstract = {We use results from zero-error information theory to project a Markov chain through a non-injective function without losing information. We show that this lossless lumping is made possible by exploiting the (sufficiently sparse) temporal structure of the Markov chain, and that our scheme is asymptotically optimal. Eliminating edges in the transition graph of the Markov chain trades the required output alphabet size versus information loss, for which we present bounds. Finally, we present a first zero-error source coding result for non-Markov processes with a deterministic dependence structure.},
 keywords = {lumping, lossless, zero-error information theory},
 msc2010 = {},
 comments = {},

 arxiv = {1509.06580},
 url = {http://arxiv.org/abs/1509.06580},
 doi = {10.1109/ISIT.2016.7541856},
}
@article{Geiger_Kubin_Temmel_Woess__EntropyInInformationTheory__TUG_2013,
 author = {Geiger, Bernhard C.
        and Kubin, Gernot
        and Temmel, Christoph
        and Woess, Wolfgang},
 title = {Entropy in {I}nformation {T}heory},
 language = {Deutsch,English},

 year = {2013},

 abstract = {},
 keywords = {},
 comments = {},

 publisher = {TU Graz},
 journal = {TU Graz Research},
 number = {9},
 volume = {1},
 pages = {19--21},
 url = {portal.tugraz.at/portal/page/portal/Files/BDR/Oeffentlichkeit/Zeitschriften/research_9_2013.pdf},
 url = {http://temmel.me/pub/Geiger_Kubin_Temmel_Woess__EntropyInInformationTheory__TUG_2013.pdf},
}
@INPROCEEDINGS{Geiger_Temmel__InformationPreservingMarkovAggregation__ITW_2013,
 author = {Geiger, Bernhard C.
       and Temmel, Christoph},
 title = {Information-preserving {M}arkov aggregation},
 language = {English},

 year = {2013},

 publisher = {IEEE},
 booktitle = {Information Theory Workshop (ITW)},
 pages = {1-5},
 isbn = {978-1-4799-1321-3},
 inspec = {14000148},

 abstract = {We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging states or, equivalently, lossless compression of a Markov source on a sample-by-sample basis. The cardinality of the reduced state space is bounded from below by the node degrees of the transition graph associated with the original Markov chain. We also present an algorithm listing all possible information-preserving state space reductions, for a given transition graph. We illustrate our results by applying the algorithm to a bi-gram letter model of an English text.},
 keywords = {lossless compression, Markov chain, model order reduction,n-gram model},
 comments = {},

 doi = {10.1109/ITW.2013.6691265},
 arxiv = {1304.0920},
 url = {http://arxiv.org/abs/1304.0920},
}
@article{Geiger_Temmel__LumpingsOfMarkovChainsEntropyRatePreservationAndHigherOrderLumpability__JAP_2014,
 author = {Geiger, Bernhard C.
        and Temmel, Christoph},
 title = {Lumpings of {M}arkov chains, entropy rate preservation, and higher-order lumpability},
 language = {English},

 year = {2014},

 publisher = {Applied Probability Trust},
 fjournal = {Journal of Applied Probability},
 journal = {J. Appl. Probab.},
 volume = {51},
 number = {4},
 pages = {1114--1132},
 issn = {0021-9002},

 abstract = {A lumping of a Markov chain is a coordinatewise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the cardinality of the realisable preimage of a finite-length trajectory of the lumped chain and by the information needed to reconstruct original trajectories from their lumped images. Both are purely combinatorial criteria, depending only on the transition graph of the Markov chain and the lumping function. A lumping is strongly k-lumpable, if and only if the lumped process is a kth-order Markov chain for each starting distribution of the original Markov chain. We characterise strong k-lumpability via tightness of stationary entropic bounds. In the sparse setting, we give sufficient conditions on the lumping to both preserve the entropy rate and be strongly k-lumpable. },
 keywords = {},
 msc2010 = {60J10 (60G10 60G17 65C40 94A17)},
 comments = {},

 mrnumber = {3301292},
 zbmath = {06408807},
 doi = {10.1239/jap/1421763331},
 arxiv = {1212.4375},
 url = {http://arxiv.org/abs/1212.4375},
}
@article {HoferTemmel__DisagreementPercolationForTheHardSphereModel__EJP_2019,
 author = {Hofer-Temmel, Christoph and Houdebert, Pierre},
 title = {Disagreement percolation for the hard-sphere model},
 language = {English},

 publisher = {The Institute of Mathematical Statistics and the Bernoulli Society},
 fjournal = {Electronic Journal of Probability},
 journal = {EJP},
 volume = {24},
 number = {91},
 pages = {1--22},
 issn = {1083-6489},
 year = {2019},

 url = {http://arxiv.org/abs/1507.02521},

 abstract = {Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure.
This work generalises disagreement percolation to the hard-sphere model and the Boolean model.
Non-percolation of the Boolean model implies the uniqueness of the Gibbs measure and exponential decay of pair correlations and finite volume errors.
Hence, lower bounds on the critical intensity for percolation of the Boolean model imply lower bounds on the critical activity for a (potential) phase transition.
These lower bounds improve upon known bounds obtained by cluster expansion techniques.
The proof uses a novel dependent thinning from a Poisson point process to the hard-sphere model, with the thinning probability related to a derivative of the free energy.
},
 keywords = {hard-sphere model,
disagreement percolation,
unique Gibbs measure,
stochastic domination,
Boolean model,
absence of phase transition,
dependent thinning
},
 msc2010 = {82B21 (60E15 60K35 60G55 82B43 60D05)},
 comments = {},

 zbmath = {},
 mr = {},
 doi = {doi.org/10.1214/19-EJP320},
 arxiv = {1507.02521},
}
@article {HoferTemmel_Houdebert__DisagreementPercolationForGibbsBallModels__SPA_2019,
 author = {Hofer-Temmel, Christoph and Houdebert, Pierre},
 title = {Disagreement percolation for Gibbs ball models},
 language = {English},

 publisher = {Elsevier},
 fjournal = {Stochastic Processes and their Applications},
 journal = {Stochastic Process. Appl.},
 volume = {129},
 number = {10},
 pages = {3922-3940},
 issn = {0304-4149},
 coden = {STOPB7},
 year = {2019},

 url = {http://arxiv.org/abs/1709.04286},

 abstract = {We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of pair correlations in the low activity regime by comparison with a sub-critical Boolean model. Applications to the Continuum Random Cluster model and the Quermass-interaction model are presented. At the core of our proof lies an explicit dependent thinning from a Poisson point process to a dominated Gibbs point process.
},
 keywords = {Continuum random cluster model
Disagreement percolation
Dependent thinning
Boolean model
Stochastic domination
Phase transition
Unique Gibbs state
Exponential decay of pair correlation
},
 msc2010 = {82B21, 60E15, 60K35, 60G55, 82B43, 60D05},
 comments = {},

 zbmath = {},
 mr = {},
 doi = {10.1016/j.spa.2018.11.003},
 arxiv = {1709.04286},
}
@article{HoferTemmel_Lehner__CliqueTreesOfInfiniteLocallyFiniteChordalGraphs__EJC_2018,
 author = {Hofer-Temmel, Christoph
       and Lehner, Florian},
 title = {Clique trees of infinite, locally finite chordal graphs},
 language = {English},

 year = {2018},
 JOURNAL = {Electron. J. Combin.},
 FJOURNAL = {Electronic Journal of Combinatorics},
 volume = {25},
 issue = {2},
 page = {Paper 2.9, 25},
 ISSN = {},

 abstract = {We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are in bijection with the edges of the corresponding collection of finite trees. This allows us to enumerate the clique trees of a chordal graph and extend various classic characterisations of clique trees to the infinite setting.},
 keywords = {chordal graph, clique tree, minimal separator, Lovász Local Lemma, 1-dependent colouring},
 msc2010 = {05C62 (05C05 05C30)},
 MRNUMBER = {3799427},
 comments = {},

 arxiv = {1311.7001},
 url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i2p9},
}
@article {HoferTemmel__ShearersPointProcessTheHardSphereModelAndAcontinuumLovaszLocalLemma__AdvAppPro_2017,
    AUTHOR = {Hofer-Temmel, Christoph},
     TITLE = {Shearer's point process, the hard-sphere model, and a
              continuum {L}ov\'asz local lemma},
   JOURNAL = {Adv. in Appl. Probab.},
  FJOURNAL = {Advances in Applied Probability},
    VOLUME = {49},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {1--23},
      ISSN = {0001-8678},
   MRCLASS = {60G55 (05D99 60G60 82B05)},
  MRNUMBER = {3631213},
       URL = {http://arxiv.org/abs/1312.0850},
 abstract = {A point process is R-dependent, if it behaves independently beyond the minimum distance R. We investigate uniform positive lower bounds on the avoidance functions of R-dependent simple point processes of the same intensity. Such bounds hold, iff Shearer's point process, the unique R-dependent point process with an R-hard-core, exists. The continuum Lovász Local Lemma is a sufficient condition on the intensity and R to guarantee uniform exponential lower bounds on the avoidance function for all R-dependent point processes of this intensity. Shearer's point process shares combinatorial structure with the hard-sphere model with radius R, the unique Markov point process with an R-hard-core and range R interaction. We obtain a lower bound on the radius of convergence of a high-temperature cluster expansion of the hard-sphere model and recover a classic result of Ruelle via an inductive approach à la Dobrushin.},
  doi = {10.1017/apr.2016.76},
  arxiv = {1312.0850},
}
@article {Mathieu_Temmel__KIndependentPercolationOnTrees__SPA_2012,
 author = {Mathieu, Pierre
        and Temmel, Christoph},
 title = {{$k$}-independent percolation on trees},
 language = {English},

 year = {2012},

 publisher = {Elsevier},
 fjournal = {Stochastic Processes and their Applications},
 journal = {Stochastic Process. Appl.},
 volume = {122},
 number = {3},
 pages = {1129--1153},
 issn = {0304-4149},
 coden = {STOPB7},

 abstract = {Consider the class of k-independent bond or site percolations with parameter p on a tree T. We derive tight bounds on p for both almost sure percolation and nonpercolation. The bounds are continuous functions of k and the branching number of T. This extends previous results by Lyons for the independent case and by Balister & Bollobas for 1-independent bond percolations. Central to our argumentation are moment method bounds à la Lyons supplemented by explicit percolation models à la Balister & Bollobas. An indispensable tool is the minimality and explicit construction of Shearer's measure on the k-fuzz of Z.},
 keywords = {k-independent; k-dependent; tree percolation; critical value; percolation kernel; second moment method; Shearer’s measure},
 msc2010 = {82B43 (60K35 05C05 05C80)},
 comments = {},

 mrnumber = {2891450},
 zbmath = {06017617},
 doi = {10.1016/j.spa.2011.10.014},
 arxiv = {1103.1291},
 url = {http://arxiv.org/abs/1103.1291},
}
@unpublished {HoferTemmel__LimitsAndLimitationsOfClusterExpansionInTheHardSphereModel,
 author = {Hofer-Temmel, Christoph},
 title = {Limits and limitations of cluster expansion in the hard-sphere model},
 language = {English},

 year = {2015+},

 note = {In preparation},
 url = {},

 abstract = {},
 keywords = {},
 msc2010 = {},
 comments = {},

 arxiv = {},
}

@unpublished {HoferTemmel__ShearersPointProcessAndTheHardSphereModelInOneDimension,
 author = {Hofer-Temmel, Christoph},
 title = {Shearer's point process and the hard-sphere model in one dimension},
 language = {English},

 year = {2015+},

 note = {Preprint},

 abstract = {We revisit the smallest non-physical singularity of the hard-sphere model in one dimension, also known as Tonks gas. We give an explicit expression of the free energy and reduced correlations at negative real fugacity and elaborate the nature of the singularity: the free energy is right-continuous, but its derivative diverges. We derive these results in several novel ways: First, by scaling up the discrete solution. Second, by an inductive argument on the partition function à la Dobrushin. Third, by a perfect cluster expansion counting the Penrose trees in the Mayer expansion perfectly. Fourth, by an explicit construction of Shearer's point process, the unique R-dependent point process with an R-hard-core. The last connection yields explicit and optimal lower bounds on the avoidance function of R-dependent point processes on the real line.},
 keywords = {Shearer's point process, hard-sphere model, Lovász Local Lemma, Tonks gas, cluster expansion, Lambert W function},
 msc2010 = {60G55 (82B05)},
 comments = {},

 arxiv = {1504.02672},
 url = {http://arxiv.org/abs/1504.02672},
}
@unpublished {Benes_HoferTemmel_Last_Vecera__DecorrelationOfAClassOfGibbsParticleProcessesAndAsymptoticPropertiesOfUStatistics,
 author = {Bene\v{s}, Viktor and Hofer-Temmel, Christoph and Last, G\"unter and Ve\v{c}e\v{r}a, Jakub},
 title = {Decorrelation of a class of Gibbs particle processes and asymptotic properties of U--statistics},
 language = {English},

 year = {2018+},

 note = {In preparation},
 url = {},

 abstract = {},
 keywords = {},
 msc2010 = {},
 comments = {},

 arxiv = {1903.06553},

 url = {https://arxiv.org/abs/1903.06553},
}


@mastersthesis {Temmel__KIndependentPercolationOnInfiniteTreesAfterTheWorksOfBollobasAndBalister__TUG_2008,
 author = {Temmel, Christoph},
 title = {K-independent percolation on infinite trees after the works of {B}ollob\'{a}s and {B}alister},
 language = {English},

 year = {2008},

 school = {Institut f\"{u}r Mathematische Strukturtheorie, TU Graz},

 abstract = {},
 keywords = {},
 msc2010 = {},
 comments = {Supervised by Wolfgang Woess, with a research stay with Pierre Mathieu},
 url = {http://temmel.me/Temmel__KIndependentPercolationOnInfiniteTreesAfterTheWorksOfBollobasAndBalister__TUG_2008.pdf},
}
@misc {Temmel__LaComposanteGeanteDUnGrapheAleatoire__UdP_2007,
 author = {Temmel, Christoph},
 title = {La composante g\'{e}ante d'un graphe al\'{e}atoire},
 language = {Francais},

 year = {2007},

 school = {LATP, Université de Provence},

 abstract = {},
 keywords = {},
 msc2010 = {},
 comments = {TER dans le M1 sous la direction de Pierre Mathieu},
 url = {http://temmel.me/Temmel__LaComposanteGeanteDUnGrapheAleatoire__UdP_2007.pdf},
}
@phdthesis {Temmel__PropertiesAndApplicationsOfBernoulliRandomFieldsWithStrongDependencyGraphs__TUG_2012,
 author = {Temmel, Christoph},
 title = {Properties and applications of {B}ernoulli random fields with strong dependency graphs},
 language = {English},

 year = {2012},

 school = {Institut f\"{u}r Mathematische Strukturtheorie, TU Graz},

 abstract = {},
 keywords = {},
 msc2010 = {},
 comments = {Supervised by Pierre Mathieu and Wolfgang Woess},
 url = {http://temmel.me/Temmel__PropertiesAndApplicationsOfBernoulliRandomFieldsWithStrongDependencyGraphs__TUG_2012.pdf},
}
@article {Temmel__ShearersMeasureAndStochasticDominationOfProductMeasures__JTP_2014,
 author = {Temmel, Christoph},
 title = {Shearer's measure and stochastic domination of product measures},
 language = {English},

 year = {2014},

 fjournal = {Journal of Theoretical Probability},
 journal = {J. Theoret. Probab.},
 volume = {27},
 number = {1},
 pages = {22--40},
 publisher = {Springer},
 issn = {0894-9840},
 coden = {},

 abstract = {Let $G=(V,E)$ be a locally finite graph. Let $\vec{p}\in[0,1]^V$. We show that Shearer’s measure, introduced in the context of the Lovász Local Lemma, with marginal distribution determined by $\vec{p}$, exists on $G$ if and only if every Bernoulli random field with the same marginals and dependency graph $G$ dominates stochastically a non-trivial Bernoulli product field. Additionally, we derive a non-trivial uniform lower bound for the parameter vector of the dominated Bernoulli product field. This generalises previous results by Liggett, Schonmann, and Stacey in the homogeneous case, in particular on the $k$-fuzz of $\mathbb{Z}$. Using the connection between Shearer’s measure and a hardcore lattice gas established by Scott and Sokal, we transfer bounds derived from cluster expansions of lattice gas partition functions to the stochastic domination problem.},
 keywords = {stochastic domination, Lovász Local Lemma, product measure
Bernoulli random field, stochastic order, hardcore lattice gas},
 msc2010 = {60E15 (60G60 82B20 05D40)},
 comments = {},

 mrnumber = {3174214},
 zbmath = {06348412},
 doi = {10.1007/s10959-012-0423-6},
 arxiv = {1105.1683},
 url = {http://arxiv.org/abs/1105.1683},
}
@article{Temmel__SufficientConditionsForUniformBoundsInAbstractPolymerSystemsAndExplorativePartitionSchemes__JSP_2014,
 author = {Temmel, Christoph},
 title = {Sufficient Conditions for Uniform Bounds in Abstract Polymer Systems and Explorative Partition Schemes},
 language = {English},

 year = {2014},
 month = {},

 fjournal = {Journal of Statistical Physics},
 journal = {J. Stat. Phys.},
 publisher = {Springer},
 volume = {157},
 number = {6},
 pages = {1225-1254},
 issn = {0022-4715 (1572-9613)},

 abstract = {We present several new sufficient conditions for uniform boundedness of the reduced correlations and free energy of an abstract polymer system in a complex multidisc around zero fugacity. They resolve a discrepancy between two incomparable and previously known extensions of Dobrushin’s classic condition. All conditions arise from an extension of the tree-operator approach introduced by Fernández and Procacci combined with a novel family of partition schemes of the spanning subgraph complex of a cluster. The key technique is the increased transfer of structural information from the partition scheme to a tree-operator on an enhanced space.},
 keywords = {cluster expansion; abstract polymer system; partition scheme; tree-operator; hardcore gas},
 msc2010 = {82B20 (05A15, 47H10) 82D60},
 comments = {},

 mrnumber = {3277765},
 zbmath = {06398914},
 doi = {10.1007/s10955-014-1108-6},
 arxiv = {1209.4035},
 url = {http://arxiv.org/abs/1209.4035},
}