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作者：Rezaei, Mohammad A.; Zhan, Dapeng
作者单位：Michigan State University
摘要：For a chordal SLE () curve in a domain D, the n-point Green's function valued at distinct points is defined to be here is the Hausdorff dimension of SLE, provided that the limit converges. In this paper, we will show that such Green's functions exist for any finite number of points. Along the way we provide the rate of convergence and modulus of continuity for Green's functions as well. Finally, we give up-to-constant bounds for them.
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作者：Wang, Zhenan
作者单位：University of Washington; University of Washington Seattle
摘要：Under general conditions we show an a priori probabilistic Harnack inequality for the non-negative solution of a stochastic partial differential equation of the following form We also show that the solutions of the above equation are almost surely strictly positive if the initial condition is non-negative and not identically vanishing.
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作者：Hermon, Jonathan; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：There are several works characterizing the total-variation mixing time of a reversible Markov chain in term of natural probabilistic concepts such as stopping times and hitting times. In contrast, there is no known analog for the L-2 mixing time, tau(2) (while there are sophisticated analytic tools to bound tau(2), in general they do not determine tau(2) up to a constant factor and they lack a probabilistic interpretation). In this work we show that tau(2) can be characterized up to a constant...
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作者：Beliaev, Dmitry; Wigman, Igor
作者单位：University of Oxford; University of London; King's College London
摘要：We study the volume distribution of nodal domains of families of naturally arising Gaussian random fields on generic manifolds, namely random band-limited functions. It is found that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.
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作者：De, Anindya; Servedio, Rocco A.
作者单位：Northwestern University; Columbia University
摘要：One of the main results of this paper is a new multidimensional central limit theorem (CLT) for multivariate polynomials under Gaussian inputs. Roughly speaking, the new CLT shows that any collection of Gaussian polynomials with small eigenvalues (suitably defined) must have a joint distribution which is close to a multidimensional Gaussian distribution. The new CLT is proved using tools from Malliavin calculus and Stein's method. A second main result of the paper, which complements the new CL...
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作者：Bordenave, Charles; Caputo, Pietro; Salez, Justin
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Roma Tre University; Universite Paris Cite
摘要：A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the context of card shuffling (Aldous and Diaconis in Am Math Mon 93:333-348, 1986), this remarkable phenomenon is now rigorously established for many reversible chains. Here we consider the non-reversible case of random walks on sparse directed graphs, for whi...
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作者：Coca, Alberto J.
作者单位：University of Cambridge
摘要：A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L,vy distributions are proposed and functional central limit theorems using the uniform norm are proved for both under mild conditions. The limiting Gaussian processes are identified and efficiency of the estimators is established. Kernel estimators for the mass function, the intensity and the drift are also proposed, their asymptotic properties in...
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作者：Sapozhnikov, Artem; Shiraishi, Daisuke
作者单位：Leipzig University; Kyoto University
摘要：We provide a decomposition of the trace of the Brownian motion into a simple path and an independent Brownian soup of loops that intersect the simple path. More precisely, we prove that any subsequential scaling limit of the loop erased random walk is a simple path (a new result in three dimensions), which can be taken as the simple path of the decomposition. In three dimensions, we also prove that the Hausdorff dimension of any such subsequential scaling limit lies. We conjecture that our dec...
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作者：Lee, Ji Oon; Schnelli, Kevin
作者单位：Korea Advanced Institute of Science & Technology (KAIST); Royal Institute of Technology; Institute of Science & Technology - Austria
摘要：We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the ErdAs-R,nyi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy-Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency ma...
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作者：Deuschel, Jean-Dominique; Tuan Anh Nguyen; Slowik, Martin
作者单位：Technical University of Berlin
摘要：We consider a stationary and ergodic random field that is parameterized by the edge set of the Euclidean lattice , . The random variable , taking values in and satisfying certain moment bounds, is thought of as the conductance of the edge e. Assuming that the set of edges with positive conductances give rise to a unique infinite cluster , we prove a quenched invariance principle for the continuous-time random walk among random conductances under certain moment conditions. An essential ingredie...
