@book{ZassZagrebnovSukiasyanetal.2020, author = {Zass, Alexander and Zagrebnov, Valentin and Sukiasyan, Hayk and Melkonyan, Tatev and Rafler, Mathias and Poghosyan, Suren and Zessin, Hans and Piatnitski, Andrey and Zhizhina, Elena and Pechersky, Eugeny and Pirogov, Sergei and Yambartsev, Anatoly and Mazzonetto, Sara and Lykov, Alexander and Malyshev, Vadim and Khachatryan, Linda and Nahapetian, Boris and Jursenas, Rytis and Jansen, Sabine and Tsagkarogiannis, Dimitrios and Kuna, Tobias and Kolesnikov, Leonid and Hryniv, Ostap and Wallace, Clare and Houdebert, Pierre and Figari, Rodolfo and Teta, Alessandro and Boldrighini, Carlo and Frigio, Sandro and Maponi, Pierluigi and Pellegrinotti, Alessandro and Sinai, Yakov G.}, title = {Proceedings of the XI international conference stochastic and analytic methods in mathematical physics}, number = {6}, editor = {Roelly, Sylvie and Rafler, Mathias and Poghosyan, Suren}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-45919}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-459192}, publisher = {Universit{\"a}t Potsdam}, pages = {xiv, 194}, year = {2020}, abstract = {The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 - 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol'fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.}, language = {en} } @article{HoudebertZass2022, author = {Houdebert, Pierre and Zass, Alexander}, title = {An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions}, series = {Journal of applied probability / Applied Probability Trust}, volume = {59}, journal = {Journal of applied probability / Applied Probability Trust}, number = {2}, publisher = {Cambridge Univ. Press}, address = {Cambridge}, issn = {0021-9002}, doi = {10.1017/jpr.2021.70}, pages = {541 -- 555}, year = {2022}, abstract = {We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity z and inverse temperature beta. The technique used relies on applying to the continuous setting the classical Dobrushin criterion. We also present a comparison to the two other uniqueness methods of cluster expansion and disagreement percolation, which can also be applied for this type of interaction.}, language = {en} } @article{Houdebert2020, author = {Houdebert, Pierre}, title = {Numerical study for the phase transition of the area-interaction model}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47217}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472177}, pages = {165 -- 174}, year = {2020}, language = {en} } @article{HoferTemmelHoudebert2018, author = {Hofer-Temmel, Christoph and Houdebert, Pierre}, title = {Disagreement percolation for Gibbs ball models}, series = {Stochastic processes and their application}, volume = {129}, journal = {Stochastic processes and their application}, number = {10}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0304-4149}, doi = {10.1016/j.spa.2018.11.003}, pages = {3922 -- 3940}, year = {2018}, 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. (C) 2018 Elsevier B.V. All rights reserved.}, language = {en} } @article{DereudreHoudebert2018, author = {Dereudre, David and Houdebert, Pierre}, title = {Sharp phase transition for the continuum Widom-Rowlinson model}, series = {Annales de l'Institut Henri Poincar{\´e}. B, Probability and statistics}, volume = {57}, journal = {Annales de l'Institut Henri Poincar{\´e}. B, Probability and statistics}, number = {1}, publisher = {Association des Publications de l'Institut Henri Poincar{\´e}}, address = {Bethesda, Md.}, issn = {0246-0203}, doi = {10.1214/20-AIHP1082}, pages = {387 -- 407}, year = {2018}, abstract = {The Widom-Rowlinson model (or the Area-interaction model) is a Gibbs point process in R-d with the formal Hamiltonian defined as the volume of Ux epsilon omega B1(x), where. is a locally finite configuration of points and B-1(x) denotes the unit closed ball centred at x. The model is also tuned by two other parameters: the activity z > 0 related to the intensity of the process and the inverse temperature beta >= 0 related to the strength of the interaction. In the present paper we investigate the phase transition of the model in the point of view of percolation theory and the liquid-gas transition. First, considering the graph connecting points with distance smaller than 2r > 0, we show that for any beta >= 0, there exists 0 <(similar to a)(zc) (beta, r) < +infinity such that an exponential decay of connectivity at distance n occurs in the subcritical phase (i.e. z <(similar to a)(zc) (beta, r)) and a linear lower bound of the connection at infinity holds in the supercritical case (i.e. z >(similar to a)(zc) (beta, r)). These results are in the spirit of recent works using the theory of randomised tree algorithms (Probab. Theory Related Fields 173 (2019) 479-490, Ann. of Math. 189 (2019) 75-99, Duminil-Copin, Raoufi and Tassion (2018)). Secondly we study a standard liquid-gas phase transition related to the uniqueness/non-uniqueness of Gibbs states depending on the parameters z, beta. Old results (Phys. Rev. Lett. 27 (1971) 1040-1041, J. Chem. Phys. 52 (1970) 1670-1684) claim that a non-uniqueness regime occurs for z = beta large enough and it is conjectured that the uniqueness should hold outside such an half line ( z = beta >= beta(c) > 0). We solve partially this conjecture in any dimension by showing that for beta large enough the non-uniqueness holds if and only if z = beta. We show also that this critical value z = beta corresponds to the percolation threshold (similar to a)(zc) (beta, r) = beta for beta large enough, providing a straight connection between these two notions of phase transition.}, language = {en} }