-
作者：Bauerschmidt, Roland; Park, Jiwoon; Rodriguez, Pierre -Francois
作者单位：University of Cambridge; Imperial College London
摘要：The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer -valued. In two dimensions and at sufficiently high temperature, we show that its macroscopic scaling limit on the torus is a multiple of the Gaussian free field. Our proof starts from a single renormalisation group step after which the integer -valued field becomes a smooth field, which we then analyse using the renormalisation group method. This paper also provides the foundation for the construction of ...
-
作者：Busani, Ofer; Seppalainen, Timo; Sorensen, Evan
作者单位：University of Bonn; University of Wisconsin System; University of Wisconsin Madison
摘要：The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of the Busemann process of exponential last-passage percolation. It was independently discovered as the Busemann process of Brownian last-passage percolation by the second and third authors. We show that SH is the unique invariant distribution and an attractor of the KPZ fixed point under conditions on th...
-
作者：Tourniaire, Julie
作者单位：University of Vienna
摘要：We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift - mu and killed upon reaching 0, starting with N particles. More precisely, particles branch at rate rho /2 in the interval [ 0, 1], for some rho > 1, and at rate 1/2 in (1, +infinity ). The drift mu(rho) is chosen in such a way that, heuristically, the system is critical in some sense: the number of particles stays roughly constant before it event...
-
作者：Dembo, Amir; Okada, Izumi
作者单位：Stanford University; Chiba University
摘要：We establish both the lim sup and the lim inf law of the iterated logarithm (LIL) for the capacity of the range of a simple random walk in any dimension d >= 3. While for d >= 4, the order of growth in n of such LIL at dimension d matches that for the volume of the random walk range in dimension d - 2, somewhat surprisingly this correspondence breaks down for the capacity of the range at d = 3. We further establish such LIL for the Brownian capacity of a three-dimensional Brownian sample path ...
-
作者：Iksanov, Alexander; Kolesko, Konrad; Meiners, Matthias
作者单位：Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; University of Wroclaw; Justus Liebig University Giessen
摘要：Consider a supercritical Crump-Mode-Jagers process (Z(t)(phi))(t >= 0) counted with a random characteristic phi. Nerman's celebrated law of large numbers [Z. Wahrsch. Verw. Gebiete 57, 365--395, 1981] states that, under some mild assumptions, e(-alpha t)Z(t )(phi)converges almost surely as t ->infinity to aW. Here, alpha>0 is the Malthusian parameter, a is a constant and W is the limit of Nerman's martingale, which is positive on the survival event. In this general situation, under additional ...
-
作者：Rudelson, Mark
作者单位：University of Michigan System; University of Michigan
摘要：Let A be an nxn x n random matrix with independent identically distributed nonconstant sub-Gaussian entries. Then for any k <= c ,J n , rank (A) >= n - k with probability at least 1 - exp ( - c l kn) .
-
作者：Zhang, Lingfu
作者单位：University of California System; University of California Davis
摘要：We consider the Metropolis biased card shuffling (also called the multispecies ASEP on a finite interval or the random Metropolis scan). Its convergence to stationarity was believed to exhibit a total -variation cutoff, and that was proved a few years ago by Labbe and Lacoin (Ann. Probab. 47 (2019) 1541-1586). In this paper, we prove that (for N cards) the cutoff window is in the order of N1/3, and the cutoff profile is given by the Tracy-Widom GOE distribution function. This confirms a conjec...
-
作者：Adamczak, Radoslaw; Pivovarov, Peter; Simanjuntak, Paul
作者单位：University of Warsaw; University of Missouri System; University of Missouri Columbia
摘要：We establish central limit theorems for the volumes of intersections of Bpn (the unit ball of in p) with uniform random subspaces of codimension d for fixed d and n -> infinity. As a corollary we obtain higher-order approximations for expected volumes, refining previous results by Koldobsky and Lifschitz and approximations obtained from the Eldan-Klartag version of CLT for convex bodies. We also obtain a central limit theorem for the Minkowski functional of the intersection body of Bnp, evalua...
-
作者：Chen, Xin; Wang, Jian
作者单位：Shanghai Jiao Tong University; Fujian Normal University
摘要：Consider the Schrodinger operator L-V = - Delta + V on R-d , where V : R-d -> [0 , infinity) is a nonnegative and locally bounded potential on R-d so that for all x is an element of R-d with | x | >= 1, c(1)g( | x | ) <= V (x) <= c(2)g( | x | ) with some constants c 1 , c(2) > 0 and a nondecreasing and strictly positive function g : [0,infinity) -> [1 ,+infinity ) that satisfies g(2r) <= c(0)g(r) for all r > 0 and lim(r ->infinity )g(r) = infinity . We establish global in time and qualitativel...
-
作者：Lipnowski, Michael; Wright, Lex
作者单位：University System of Ohio; Ohio State University; University of Michigan System; University of Michigan
摘要：We show that the Weil-Petersson probability that a random surface has first eigenvalue of the Laplacian less than 3/16-epsilon goes to zero as the genus goes to infinity.
