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作者：MacLaurin, James
作者单位：New Jersey Institute of Technology
摘要：We study the dynamics of symmetric and asymmetric spin-glass models of size N. The analysis is in terms of the double empirical process: this contains both the spins, and the field felt by each spin, at a particular time (without any knowledge of the correlation history). It is demonstrated that in the large N limit, the dynamics of the double empirical process becomes deterministic and autonomous over finite time intervals. This does not contradict the well-known fact that SK spin-glass dynam...
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作者：Zhan, Dapeng
作者单位：Michigan State University
摘要：We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLE kappa loop measures for kappa is an element of(0,8). First, we construct rooted SLE kappa loop measures in the Riemann sphere (C) over cap, which satisfy Mobius covariance, conformal Markov property, reversibility, and space-time homogeneity, when the loop is parametrized by its (1+kappa-8) -dimensional Minkowski content. Second, by integrating rooted SLE kappa loop measures, we construct the unro...
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We investigate properties of Markov quasi-diffusion processes corresponding to elliptic operators L = a(ij) D-ij + b(i) D-i, acting on functions on R-d, with measurable coefficients, bounded and uniformly elliptic a and b is an element of L-d (R-d). We show that each of them is strong Markov with strong Feller transition semigroup T-t, which is also a continuous bounded semigroup in L-d0 (R-d) for some d(0) is an element of (d/2, d). We show that T-t, t > 0, has a kernel p(t)(x, y) which is su...
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作者：Basak, Anirban; Rudelson, Mark
作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; Weizmann Institute of Science; University of Michigan System; University of Michigan
摘要：We consider three models of sparse random graphs: undirected and directed Erdos-Renyi graphs and random bipartite graph with two equal parts. For such graphs, we show that if the edge connectivity probability p satisfies np >= log n + k(n) with k(n) -> infinity as n -> infinity, then the adjacency matrix is invertible with probability approaching one (n is the number of vertices in the two former cases and the same for each part in the latter case). For np <= log n -k(n) these matrices are inv...
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作者：Eberhard, Sean; Varju, Peter P.
作者单位：University of Cambridge
摘要：Define (X-n) on Z/qZ by Xn+1 = 2X(n) + b(n), where the steps b(n) are chosen independently at random from -1, 0,+1. The mixing time of this random walk is known to be at most 1.02 log(2) q for almost all odd q (Chung, Diaconis, Graham in Ann Probab 15(3):1148-1165, 1987), and at least 1.004 log(2) q (Hildebrand in Proc Am Math Soc 137(4):1479-1487, 2009). We identify a constant c = 1.01136 ... such that the mixing time is (c + o(1)) log(2) q for almost all odd q. In general, the mixing time of...
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作者：Friz, Peter K.; Tran, Huy; Yuan, Yizheng
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：Schramm-Loewner evolution (SLE kappa) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by root kappa times Brownian motion. This yields a (half-plane) valued random field gamma = gamma (t, kappa;omega). (Holder) regularity of in gamma (center dot, kappa; omega), a.k.a. SLE trace, has been considered by many authors, starting with Rohde and Schramm (Ann Math (2) 161(2):883-924, 2005). Subsequently, Johansson Viklund et al. (Probab Theory Relat Fields...
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作者：Augeri, Fanny
摘要：We develop transportation-entropy inequalities which are saturated by measures such that their log-density with respect to the background measure is an affine function, in the setting of the uniform measure on the discrete hypercube and the exponential measure. In this sense, this extends the well-known result of Talagrand in the Gaussian case. By duality, these transportation-entropy inequalities imply a strong integrability inequality for Bernoulli and exponential processes. As a result, we ...
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作者：Angel, Omer; Hutchcroft, Tom; Jarai, Antal
作者单位：University of British Columbia; University of Cambridge; University of Bath
摘要：Consider a critical branching random walk on Z(d), d >= 1, started with a single particle at the origin, and let L(x) be the total number of particles that ever visit a vertex x. We study the tail of L(x) under suitable conditions on the offspring distribution. In particular, our results hold if the offspring distribution has an exponential moment.
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作者：Jego, Antoine
作者单位：University of Vienna
摘要：Brownian multiplicative chaos measures, introduced in Jego (Ann Probab 48:15971643, 2020), Aidekon et al. (Ann Probab 48(4):1785-1825, 2020) and Bass et al. (Ann Probab 22:566-625, 1994), are random Borel measures that can be formally defined by exponentiating. times the square root of the local times of planar Brownian motion. So far, only the subcritical measures where the parameter gamma is less than 2 were studied. This article considers the critical case where gamma = 2, using three diffe...
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作者：Forien, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the system towards the critical point. Using the finite-size scaling results of Cerf and Messikh (Theory Relat Fields 150(1-2):193-217, 2011. ), we show that, when the size of the box grows to infinity, the temperature concentrates around the critical temperature of...
