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作者：Adhikari, Arka; Cao, Sky
作者单位：Stanford University; Massachusetts Institute of Technology (MIT)
摘要：In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables.
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作者：Bresar, Miha; Mijatovic, Aleksandar; Wade, Andrew
作者单位：University of Warwick; Durham University
摘要：We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the domain that separate stability, null recurrence and transience. In the stable case, we prove existence and uniqueness of the invariant distribution and establish the polynomial rate of decay of its tail. We also establish matching polynomial upper and lower boun...
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作者：Borga, Jacopo; Boutillier, Cedric; Feray, Valentin; Meliot, Pierre-Loic
作者单位：Stanford University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Universite Paris Saclay
摘要：We obtain scaling and local limit results for large random Young tableaux of fixed shape )0 via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: - an explicit description of the limiting surface of a uniform random Young tableau of shape )0, based on solving a complex-valued polynomial equation, - a simple criteria to determine if the limiting surface is continuous in the whole domain, - and a local limit result in the bulk of a...
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作者：Liu, Mingchang; Peltola, Eveliina; Wu, Hao
作者单位：Royal Institute of Technology; University of Bonn; Tsinghua University
摘要：We find explicit SLE(8) partition functions for the scaling limits of Peano curves in the uniform spanning tree (UST) in topological polygons with general boundary conditions. They are given in terms of Coulomb gas integral formulas, which can also be expressed in terms of determinants involving a-periods of a hyperelliptic Riemann surface. We also identify the crossing probabilities for the UST Peano curves as ratios of these partition functions. The partition functions are interpreted as cor...
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作者：Dubroff, Quentin; Kahn, Jeff
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Proving a 2009 conjecture of Itai Benjamini, we show: Theorem. For any C there is an epsilon > 0 such that for any simple graph G on V of size n, and X-0, ... an ordinary random walk on G, P ({ X- 0 ,...,X (C n )} = V ) < e (- epsilon n) . A first ingredient in the proof of this is a similar statement for Markov chains in which all transition probabilities are sufficiently small relative to C .
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作者：Catellier, Remi; Duboscq, Romain
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely nondeterminism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion B(H )for H > (1) (4), we prove that the drift may be taken to be kappa > 0 H & ouml;lder continuous and bounded for kappa > (3)(2) - (1) (2H) ...
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作者：Ji, Hong chang; Park, Jaewhi
作者单位：Institute of Science & Technology - Austria; Korea Advanced Institute of Science & Technology (KAIST)
摘要：We consider fluctuations of the largest eigenvalues of the random matrix model A + UBU* where A and B are N x N deterministic Hermitian (or symmetric) matrices and U is a Haar-distributed unitary (or orthogonal) matrix. We prove that the largest eigenvalue weakly converges to the GUE (or GOE) Tracy-Widom distribution, under mild assumptions on A and B to guarantee that the density of states of the model decays as square root around the upper edge. Our proof is based on the comparison of the Gr...
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作者：Salins, Michael
作者单位：Boston University
摘要：We investigate the finite time explosion of the stochastic heat equation (partial derivative u)/(partial derivative t)=Delta u(t,x)+sigma(u(t,x))W-center dot(t,x) in the critical setting where sigma grows like sigma(u)approximate to C(1+|u|(gamma)) and gamma=(3)/(2). Mueller previously identified gamma=(3)/(2) as the critical growth rate for explosion and proved that solutions cannot explode in finite time if gamma<(3)/(2) and solutions will explode with positive probability if gamma>(3)/(2). ...
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作者：LE Gall, JEAN-FRANcOIS; Perkins, Edwin
作者单位：Universite Paris Saclay; University of British Columbia
摘要：We show that local times of super-Brownian motion, or of Brownian motion indexed by the Brownian tree, satisfy an explicit stochastic differential equation. Our proofs rely on both excursion theory for the Brownian snake and tools from the theory of superprocesses.
