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作者：Neuman, Eyal
作者单位：Imperial College London
摘要：We study the solutions of the stochastic heat equation driven by spatially inhomogeneous multiplicative white noise based on a fractal measure. We prove pathwise uniqueness for solutions of this equation when the noise co-efficient is Holder continuous of index gamma > 1 - eta/2(eta+1). Here eta is an element of (0, 1) is a constant that defines the spatial regularity of the noise.
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作者：Banerjee, Sayan; Gordina, Maria; Mariano, Phanuel
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Connecticut
摘要：We construct a non-Markovian coupling for hypoelliptic diffusions which are Brownian motions in the three-dimensional Heisenberg group. We then derive properties of this coupling such as estimates on the coupling rate, and upper and lower bounds on the total variation distance between the laws of the Brownian motions. Finally, we use these properties to prove gradient estimates for harmonic functions for the hypoelliptic Laplacian which is the generator of Brownian motion in the Heisenberg gro...
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作者：Garban, Christophe; Pete, Gabor; Schramm, Oded
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Budapest University of Technology & Economics; Microsoft
摘要：We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on a version of the triangular lattice in the complex plane have unique scaling limits, which are invariant under rotations, scalings, and, in the case of the MST, also under translations. However, they are not expected to be conformally invariant. We also prove some geometric properties of the limiting MST. The topology of convergence is the space of spanning trees introduced by Aizenman et al. [Random Structures Algori...
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作者：Kolesnikov, Alexander, V; Milman, Emanuel
作者单位：HSE University (National Research University Higher School of Economics); Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：What is the optimal way to cut a convex bounded domain K in Euclidean space (R-n, vertical bar . vertical bar) into two halves of equal volume, so that the interface between the two halves has least surface area? A conjecture of Kannan, Lovasz and Simonovits asserts that, if one does not mind gaining a universal numerical factor (independent of n) in the surface area, one might as well dissect K using a hyperplane. This conjectured essential equivalence between the former nonlinear isoperimetr...
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作者：Cook, Nicholas
作者单位：California State University System; California State University Los Angeles
摘要：We obtain lower tail estimates for the smallest singular value of random matrices with independent but nonidentically distributed entries. Specifically, we consider n x n matrices with complex entries of the form M = A o X + B = (a(ij) xi(ij) + b(ij)), where X = (xi(ij)) has i.i.d. centered entries of unit variance and A and B are fixed matrices. In our main result, we obtain polynomial bounds on the smallest singular value of M for the case that A has bounded (possibly zero) entries, and B = ...
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作者：Leao, Dorival; Ohashi, Alberto; Simas, Alexandre B.
作者单位：Universidade de Sao Paulo; Universidade Federal da Paraiba
摘要：We introduce a variational theory for processes adapted to the multidimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The main novel idea is to compute the sensitivities of processes, namely derivatives of martingale components and a weak notion of infinitesimal generator, via a finite-dimensional approximation procedure based on controlled inter-arrival times and approximating ...
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作者：Nutz, Marcel; Stebegg, Florian
作者单位：Columbia University
摘要：Two probability distributions p. and v in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are allowed as transports. Much like the Hoeffding-Frechet coupling of classical transport and its symmetric counterpart, the antitone coupling, these can be characterized by order-theore...
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作者：Cammarota, Valentina; Marinucci, Domenico
作者单位：Sapienza University Rome; University of Rome Tor Vergata
摘要：We establish here a quantitative central limit theorem (in Wasserstein distance) for the Euler-Poincare characteristic of excursion sets of random spherical eigenfunctions in dimension 2. Our proof is based upon a decomposition of the Euler-Poincare characteristic into different Wiener-chaos components: we prove that its asymptotic behaviour is dominated by a single term, corresponding to the chaotic component of order two. As a consequence, we show how the asymptotic dependence on the thresho...
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作者：Rosinski, Jan
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We propose isomorphism-type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with random translations. The applicability of such tools relies on precise understanding of Levy measures of infinitely divisible processes and their representations, which are studied here in full generality. We illustrate this approach on examples of squared Bess...
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作者：Toth, Balint
作者单位：University of Bristol; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：We prove the quenched version of the central limit theorem for the displacement of a random walk in doubly stochastic random environment, under the H-1-condition, with slightly stronger, L2+epsilon (rather than L-2) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the nonreversible, divergence-free drift case, with unbounded (L2+epsilon) stream tensor. This paper is a sequel of [Ann. Probab. 45 (2017) 4307-4347] and relies on technical results quoted fr...
