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作者：Le Jan, Yves; Raimond, Olivier
作者单位：Universite Paris Saclay
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作者：Augeri, Fanny
作者单位：Weizmann Institute of Science
摘要：We prove general nonlinear large deviation estimates similar to Chatterjee-Dembo's original bounds, except that we do not require any second order smoothness. Our approach relies on convex analysis arguments and is valid for a broad class of distributions. Our results are then applied in three different setups. Our first application consists in the mean-field approximation of the partition function of the Ising model under an optimal assumption on the spectra of the adjacency matrices of the s...
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作者：Chong, Carsten; Kevei, Peter
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Szeged University
摘要：We examine the almost-sure asymptotics of the solution to the stochastic heat equation driven by a Levy space-time white noise. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short time intervals, even in the case of additive noise, which leads to a breakdown of an intuitively expected strong law of large numbers. More precisely, if we normalize the solution by an increasing nonnegative function, we either obtain convergen...
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作者：Gwynne, Ewain; Pfeffer, Joshua
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：We study the adjacency graph of bubbles, that is, complementary connected components of a SLE kappa curve for kappa is an element of (4, 8), with two such bubbles considered to be adjacent if their boundaries intersect. We show that this ad- jacency graph is a.s. connected for kappa is an element of (4, kappa(0)], where kappa(0) approximate to 5.6158 is defined explicitly. This gives a partial answer to a problem posed by Duplantier, Miller and Sheffield (2014). Our proof in fact yields a stro...
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作者：Athreya, Siva; Butkovsky, Oleg; Mytnik, Leonid
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technion Israel Institute of Technology
摘要：We consider the stochastic differential equation dX(t) = b(X-t) dt + dL(t), where the drift b is a generalized function and L is a symmetric one dimensional alpha-stable Levy processes, alpha is an element of (1, 2). We define the notion of solution to this equation and establish strong existence and uniqueness whenever b belongs to the Besov-Holder space C-beta for beta > 1/2 - alpha 1/2.
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作者：Carlen, Eric; Carvalho, Maria; Loss, Michael
作者单位：Rutgers University System; Rutgers University New Brunswick; Universidade de Lisboa; University System of Georgia; Georgia Institute of Technology
摘要：We develop a method for producing estimates on the spectral gaps of reversible Markov jump processes with chaotic invariant measures, that is effective in the case of degenerate jump rates, and we apply it to prove the Kac conjecture for hard sphere collision in three dimensions.
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作者：Saksman, Eero; Webb, Christian
作者单位：University of Helsinki; Aalto University
摘要：We prove that if omega is uniformly distributed on [0, 1], then as T -> infinity, t bar right arrow zeta (i omega T + it + 1/2) converges to a nontrivial random generalized function, which in turn is identified as a product of a very well-behaved random smooth function and a random generalized function known as a complex Gaussian multiplicative chaos distribution. This demonstrates a novel rigorous connection between probabilistic number theory and the theory of multiplicative chaos-the latter...
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作者：Banderier, Cyril; Marchal, Philippe; Wallner, Michael
作者单位：Universite Paris 13; Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux
摘要：Polya urns are urns where at each unit of time a ball is drawn and replaced with some other balls according to its colour. We introduce a more general model: the replacement rule depends on the colour of the drawn ball and the value of the time (mod p). We extend the work of Flajolet et al. on Polya urns: the generating function encoding the evolution of the urn is studied by methods of analytic combinatorics. We show that the initial partial differential equations lead to ordinary linear diff...
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作者：Raoufi, Aran
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that at any inverse temperature beta and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. The theorem is equivalent with the differentiability of the free energy with respect to the temperature at any temperature. This is obtained for a general class of interactions, that is automorphism-invariant and irreducible coupling constants. The proof uses the random current represen...
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作者：Kajino, Naotaka; Murugan, Mathav
作者单位：Kobe University; University of British Columbia
摘要：We show that, for a strongly local, regular symmetric Dirichlet form over a complete, locally compact geodesic metric space, full off-diagonal heat kernel estimates with walk dimension strictly larger than two (sub-Gaussian estimates) imply the singularity of the energy measures with respect to the symmetric measure, verifying a conjecture by M. T. Barlow in (Contemp. Math. 338 (2003) 11-40). We also prove that in the contrary case of walk dimension two, that is, where full off-diagonal Gaussi...
