Probability Theory and Related Fields

最新文章

• On Brownian motion, simple paths, and loops AI翻译
  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...
• Local law and Tracy-Widom limit for sparse random matrices AI翻译
  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...
• Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights AI翻译
  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...
• Delocalising the parabolic Anderson model through partial duplication of the potential AI翻译
  作者：Muirhead, Stephen; Pymar, Richard; Sidorova, Nadia
  作者单位：University of Oxford; University of London; University College London; University of London; University College London; University of London; Birkbeck University London
  摘要：The parabolic Anderson model on with i.i.d. potential is known to completely localise if the distribution of the potential is sufficiently heavy-tailed at infinity. In this paper we investigate a modification of the model in which the potential is partially duplicated in a symmetric way across a plane through the origin. In the case of potential distribution with polynomial tail decay, we exhibit a surprising phase transition in the model as the decay exponent varies. For large values of the e...
• Non-universality for first passage percolation on the exponential of log-correlated Gaussian fields AI翻译
  作者：Ding, Jian; Zhang, Fuxi
  作者单位：University of Chicago; Peking University
  摘要：We consider first passage percolation (FPP) where the vertex weight is given by the exponential of two-dimensional log-correlated Gaussian fields. Our work is motivated by understanding the discrete analog for the random metric associated with Liouville quantum gravity (LQG), which roughly corresponds to the exponential of a two-dimensional Gaussian free field (GFF). The particular focus of the present paper is an aspect of universality for such FPP among the family of log-correlated Gaussian ...
• How to determine if a random graph with a fixed degree sequence has a giant component AI翻译
  作者：Joos, Felix; Perarnau, Guillem; Rautenbach, Dieter; Reed, Bruce
  作者单位：University of Birmingham; Ulm University; Centre National de la Recherche Scientifique (CNRS); Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
  摘要：For a fixed degree sequence , let be a uniformly chosen (simple) graph on where the vertex i has degree . In this paper we determine whether has a giant component with high probability, essentially imposing no conditions on . We simply insist that the sum of the degrees in which are not 2 is at least for some function going to infinity with n. This is a relatively minor technical condition, and when does not satisfy it, both the probability that has a giant component and the probability that h...
• An invariance principle for sums and record times of regularly varying stationary sequences AI翻译
  作者：Basrak, Bojan; Planinic, Hrvoje; Soulier, Philippe
  作者单位：University of Zagreb; Universite Paris Saclay
  摘要：We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of point process convergence theorem. It is designed to preserve the entire information about the temporal ordering of observations which is typically lost in the limit after time scaling. By going beyond the existing asymptotic theory, we are able to prove a new...
• Interlacing adjacent levels of β-Jacobi corners processes AI翻译
  作者：Gorin, Vadim; Zhang, Lingfu
  作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; Princeton University
  摘要：We study the asymptotics of the global fluctuations for the difference between two adjacent levels in the extension of the classical Jacobi ensemble of random matrices). The limit is identified with the derivative of the 2d Gaussian free field. Our main tools are integral forms for the (Macdonald-type) difference operators originating from the shuffle algebra.
• Hypocoercivity in metastable settings and kinetic simulated annealing AI翻译
  作者：Monmarche, Pierre
  作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Universite Gustave-Eiffel
  摘要：Combining classical arguments for the analysis of the simulated annealing algorithm with the more recent hypocoercive method of distorted entropy, we prove the convergence for large time of the kinetic Langevin annealing with logarithmic cooling schedule.
• On the extreme values of the Riemann zeta function on random intervals of the critical line AI翻译
  作者：Najnudel, Joseph
  作者单位：University System of Ohio; University of Cincinnati
  摘要：In the present paper, we show that under the Riemann hypothesis, and for fixed h, epsilon > 0, the supremum of the real and the imaginary parts of log.(1/ 2 + i t) for t. [ UT -h, UT + h] are in the interval [(1 -epsilon) log log T, (1 + epsilon) log log T] with probability tending to 1 when T goes to infinity, U being a uniform random variable in [ 0, 1]. This proves a weak version of a conjecture by Fyodorov, Hiary and Keating, which has recently been intensively studied in the setting of ra...