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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：Doering, Leif; Kyprianou, Andreas E.
作者单位：University of Mannheim; University of Bath
摘要：In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on - infinity <= a < b <= infinity in terms of their ability to access the boundary (Feller's test for explosions) and to enter the interior from the boundary. Feller's technique is restricted to diffusion processes as the corresponding differential generators allow explicit computations and the use of Hille-Yosida theory. In the present article, we study exit and entrance from infinity for the most na...
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作者：Guionnet, Alice; Husson, Jonathan
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
摘要：In this article, we consider random Wigner matrices, that is, symmetric matrices such that the subdiagonal entries of X-n are independent, centered and with variance one except on the diagonal where the entries have variance two. We prove that, under some suitable hypotheses on the laws of the entries, the law of the largest eigenvalue satisfies a large deviation principle with the same rate function as in the Gaussian case. The crucial assumption is that the Laplace transform of the entries m...
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作者：Chiarini, Alberto; Nitzschner, Maximilian
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We investigate percolation of the vacant set of random interlacements on Z(d), d >= 3, in the strongly percolative regime. We consider the event that the interlacement set at level u disconnects the discrete blow-up of a compact set A subset of R-d from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of the occupation times deviate from a specific function depending on the harmonic potential of A, when disconnection...
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作者：Nadtochiy, Sergey; Shkolnikov, Mykhaylo
作者单位：Illinois Institute of Technology; Princeton University; Princeton University
摘要：Building on the line of work (Ann. Appl. Probab. 25 (2015) 2096-2133; Stochastic Process. Appl. 125 (2015) 2451-2492; Ann. Appl. Probab. 29 (2019) 89-129; Arch. Ration. Mech. Anal. 233 (2019) 643-699; Ann. Appl. Probab. 29 (2019) 2338-2373; Finance Stoch. 23 (2019) 535-594), we continue the study of particle systems with singular interaction through hitting times. In contrast to the previous research, we (i) consider very general driving processes and interaction functions, (ii) allow for inho...
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：We consider the KPZ equation in space dimension 2 driven by spacetime white noise. We showed in previous work that if the noise is mollified in space on scale epsilon and its strength is scaled as (beta) over cap/root vertical bar log epsilon vertical bar, then a transition occurs with explicit critical point (beta) over cap (c) = root 2 pi. Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as epsilon down arrow 0, for sufficiently small (beta) over ca...
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作者：Hong, Jieliang; Mytnik, Leonid; Perkins, Edwin
作者单位：University of British Columbia; Technion Israel Institute of Technology
摘要：We show that if partial derivative R is the boundary of the range of super-Brownian motion and dim denotes Hausdorff dimension, then with probability one, for any open set U, U boolean AND partial derivative R. not equal empty set implies dim(U boolean AND partial derivative R) = {4-2 root 2 approximate to 1.17 if d = 2, 9 - root 17/2 approximate to 2.44 if d = 3. This improves recent results of the last two authors by working with the actual topological boundary, rather than the boundary of t...
