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作者：Galashin, Pavel
作者单位：University of California System; University of California Los Angeles
摘要：We discover a new property of the stochastic colored six-vertex model called flip-invariance. We use it to show that for a given collection of observables of the model, any transformation that preserves the distribution of each individual observable also preserves their joint distribution. This generalizes recent shift-invariance results of Borodin-Gorin-Wheeler. As limiting cases, we obtain similar statements for the Brownian last passage percolation, the Kardar-Parisi-Zhang equation, the Air...
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作者：Deuschel, Jean-Dominique; Orenshtein, Tal; Perkowski, Nicolas
作者单位：Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Free University of Berlin
摘要：We consider additive functionals of stationary Markov processes and show that under Kipnis-Varadhan type conditions they converge in rough path topology to a Stratonovich Brownian motion, with a correction to the Levy area that can be described in terms of the asymmetry (nonreversibility) of the underlying Markov process. We apply this abstract result to three model problems: First, we study random walks with random conductances under the annealed law. If we consider the Ito rough path, then w...
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作者：Gheissari, Reza; Lubetzky, Eyal
作者单位：New York University
摘要：Consider the 3D Ising model on a box of side length n with minus boundary conditions above the xy-plane and plus boundary conditions below it. At low temperatures, Dobrushin (1972) showed that the interface separating the predominantly plus and predominantly minus regions is localized: its height above a fixed point has exponential tails. Recently, the authors proved a law of large numbers for the maximum height M-n of this interface: for every beta large, M-n/log n -> c beta in probability as...
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作者：Armstrong, Scott; Serfaty, Sylvia
作者单位：New York University
摘要：We study Coulomb gases in any dimension d >= 2 and in a broad temperature regime. We prove local laws on the energy, separation and number of points down to the microscopic scale. These yield the existence of limiting point processes after extraction, generalizing the Ginibre point process for arbitrary temperature and dimension. The local laws come together with a quantitative expansion of the free energy with a new explicit error rate in the case of a uniform background density. These estima...
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作者：Thevenin, Paul
作者单位：Uppsala University
摘要：We provide a new geometric representation of a family of fragmentation processes by nested laminations which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation, obtained by cutting a random stable tree at random points, which split the tree into smaller subtrees. When coding each of these cutpoints by a chord in the unit disk, we separate the disk into smaller connected components, corresponding to the smaller subtrees of the initial tree....
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作者：Chen, Xinxing; Dagard, Victor; Derrida, Bernard; Hu, Yueyun; Lifshits, Mikhail; Shi, Zhan
作者单位：Shanghai Jiao Tong University; Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Universite PSL; College de France; Saint Petersburg State University; Sorbonne Universite; Universite Paris Cite
摘要：We are interested in the nearly supercritical regime in a family of maxtype recursive models studied by Collet, Eckman, Glaser and Martin (Comm. Math. Phys. 94 (1984) 353-370) and by Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290) and prove that, under a suitable integrability assumption on the initial distribution, the free energy vanishes at the transition with an essential singularity with exponent 12. This gives a weaker answer to a conjecture of Derrida and Retaux (J. Stat. Phys. 1...
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作者：Ding, Jian; Fukushima, Ryoki; Sun, Rongfeng; Xu, Changji
作者单位：University of Pennsylvania; Kyoto University; National University of Singapore; University of Chicago
摘要：Place an obstacle with probability 1 - p independently at each vertex of Z(d) , and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. For d >= 2 and p strictly above the critical threshold for site percolation, we condition on the environment such that the origin is contained in an infinite connected component free of obstacles. It has previously been shown that, with high probability, the random walk conditioned on survival up to time n will be localize...
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作者：Borgs, Christian; Chayes, Jennifer T.; Dhara, Souvik; Sen, Subhabrata
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); Harvard University
摘要：We investigate structural properties of large, sparse random graphs through the lens of sampling convergence (Borgs et al. (Ann. Probab. 47 (2019) 2754-2800). Sampling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a graphex. We introduce a notion of sampling convergence for sequences of multigraphs, and establish the graphex limit for the configuration model, a preferential attachment model, the generalized random graph and a bipartite variant o...
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作者：Hartarsky, Ivailo; Martinelli, Fabio; Toninelli, Cristina
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine; Roma Tre University
摘要：In this paper, we consider kinetically constrained models (KCM) on Z(2) with general update families U. For U belonging to the so-called critical class, our focus is on the divergence of the infection time of the origin for the equilibrium process as the density of the facilitating sites vanishes. In a recent paper (Probab. Theory Related Fields 178 (2020) 289-326), Mareche and two of the present authors proved that if U has an infinite number of stable directions, then on a doubly logarithmic...
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作者：Coste, Simon; Salez, Justin
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We confirm the long-standing prediction that c = e approximate to 2.718 is the thresh-old for the emergence of a nonvanishing absolutely continuous part (extended states) at zero in the limiting spectrum of the Erdos-Renyi random graph with average degree c. This is achieved by a detailed second-order analysis of the resolvent (A - z)(-1) near the singular point z = 0, where A is the adjacency operator of the Poisson-Galton-Watson tree with mean offspring c. More generally, our method applies ...
