@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{RœllyZass2020,
  author    = {Rœlly, Sylvie and Zass, Alexander},
  title     = {Marked Gibbs point processes with unbounded interaction},
  series = {Journal of statistical physics},
  volume    = {179},
  journal   = {Journal of statistical physics},
  number    = {4},
  publisher = {Springer},
  address   = {New York},
  issn      = {0022-4715},
  doi       = {10.1007/s10955-020-02559-3},
  pages     = {972 -- 996},
  year      = {2020},
  abstract  = {We construct marked Gibbs point processes in R-d under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an a.s. finite but random range. Secondly, the random marks-attached to the locations in R-d-belong to a general normed space G. They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.},
  language  = {en}
}
@article{Zass2020,
  author    = {Zass, Alexander},
  title     = {A Gibbs point process of diffusions: Existence and uniqueness},
  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-47195},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471951},
  pages     = {13 -- 22},
  year      = {2020},
  language  = {en}
}
@phdthesis{Zass2021,
  author    = {Zass, Alexander},
  title     = {A multifaceted study of marked Gibbs point processes},
  doi       = {10.25932/publishup-51277},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-512775},
  school      = {Universit{\"a}t Potsdam},
  pages     = {vii, 104},
  year      = {2021},
  abstract  = {This thesis focuses on the study of marked Gibbs point processes, in particular presenting some results on their existence and uniqueness, with ideas and techniques drawn from different areas of statistical mechanics: the entropy method from large deviations theory, cluster expansion and the Kirkwood--Salsburg equations, the Dobrushin contraction principle and disagreement percolation. We first present an existence result for infinite-volume marked Gibbs point processes. More precisely, we use the so-called entropy method (and large-deviation tools) to construct marked Gibbs point processes in R^d under quite general assumptions. In particular, the random marks belong to a general normed space S and are not bounded. Moreover, we allow for interaction functionals that may be unbounded and whose range is finite but random. The entropy method relies on showing that a family of finite-volume Gibbs point processes belongs to sequentially compact entropy level sets, and is therefore tight. We then present infinite-dimensional Langevin diffusions, that we put in interaction via a Gibbsian description. In this setting, we are able to adapt the general result above to show the existence of the associated infinite-volume measure. We also study its correlation functions via cluster expansion techniques, and obtain the uniqueness of the Gibbs process for all inverse temperatures β and activities z below a certain threshold. This method relies in first showing that the correlation functions of the process satisfy a so-called Ruelle bound, and then using it to solve a fixed point problem in an appropriate Banach space. The uniqueness domain we obtain consists then of the model parameters z and β for which such a problem has exactly one solution. Finally, we explore further the question of uniqueness of infinite-volume Gibbs point processes on R^d, in the unmarked setting. We present, in the context of repulsive interactions with a hard-core component, a novel approach to uniqueness by applying the discrete Dobrushin criterion to the continuum framework. We first fix a discretisation parameter a>0 and then study the behaviour of the uniqueness domain as a goes to 0. With this technique we are able to obtain explicit thresholds for the parameters z and β, which we then compare to existing results coming from the different methods of cluster expansion and disagreement percolation. Throughout this thesis, we illustrate our theoretical results with various examples both from classical statistical mechanics and stochastic geometry.},
  language  = {en}
}
@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}
}