3-4期

最新文章

• The nested simple conformal loop ensembles in the Riemann sphere AI翻译
  作者：Kemppainen, Antti; Werner, Wendelin
  作者单位：University of Helsinki; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：Simple conformal loop ensembles (CLE) are random collections of simple non-intersecting loops that are of particular interest in the study of conformally invariant systems. Among other things related to these CLEs, we prove the invariance in distribution of their nested full-plane versions under the inversion z bar right arrow 1/z.
• Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions AI翻译
  作者：Andres, Sebastian; Kajino, Naotaka
  作者单位：University of Bonn; Kobe University
  摘要：The Liouville Brownian motion (LBM), recently introduced by Garban, Rhodes and Vargas and in a weaker form also by Berestycki, is a diffusion process evolving in a planar random geometry induced by the Liouville measure , formally written as , , for a (massive) Gaussian free field X. It is an -symmetric diffusion defined as the time change of the two-dimensional Brownian motion by the positive continuous additive functional with Revuz measure . In this paper we provide a detailed analysis of t...
• The Brownian Conga line AI翻译
  作者：Banerjee, Sayan
  作者单位：University of Warwick
  摘要：We introduce a new model called the Brownian Conga line. It is a random curve evolving in time, generated when a particle performing a two dimensional Gaussian random walk leads a long chain of particles connected to each other by cohesive forces. We approximate the discrete Conga line in some sense by a smooth random curve and subsequently study the properties of this smooth curve.
• Community detection in sparse networks via Grothendieck's inequality AI翻译
  作者：Guedon, Olivier; Vershynin, Roman
  作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; University of Michigan System; University of Michigan
  摘要：We present a simple and flexible method to prove consistency of semidefinite optimization problems on random graphs. The method is based on Grothendieck's inequality. Unlike the previous uses of this inequality that lead to constant relative accuracy, we achieve any given relative accuracy by leveraging randomness. We illustrate the method with the problem of community detection in sparse networks, those with bounded average degrees. We demonstrate that even in this regime, various simple and ...
• Scalar conservation laws with monotone pure-jump Markov initial conditions AI翻译
  作者：Kaspar, David C.; Rezakhanlou, Fraydoun
  作者单位：Brown University; University of California System; University of California Berkeley
  摘要：In 2010 Menon and Srinivasan published a conjecture for the statistical structure of solutions to scalar conservation laws with certain Markov initial conditions, proposing a kinetic equation that should suffice to describe as a stochastic process in x with t fixed. In this article we verify an analogue of the conjecture for initial conditions which are bounded, monotone, and piecewise constant. Our argument uses a particle system representation of over for , with a suitable random boundary co...
• On singularity as a function of time of a conditional distribution of an exit time AI翻译
  作者：Krylov, N. V.
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：We establish the singularity with respect to Lebesgue measure as a function of time of the conditional probability distribution that the sum of two one-dimensional Brownian motions will exit from the unit interval before time t, given the trajectory of the second Brownian motion up to the same time. On the way of doing so we show that if one solves the one-dimensional heat equation with zero condition on a trajectory of a one-dimensional Brownian motion, which is the lateral boundary, then for...
• Dimension of fractional Brownian motion with variable drift AI翻译
  作者：Peres, Yuval; Sousi, Perla
  作者单位：Microsoft; University of Cambridge
  摘要：Let X be a fractional Brownian motion in . For any Borel function , we express the Hausdorff dimension of the image and the graph of in terms of f. This is new even for the case of Brownian motion and continuous f, where it was known that this dimension is almost surely constant. The expression involves an adaptation of the parabolic dimension previously used by Taylor and Watson to characterize polarity for the heat equation. In the case when the graph of f is a self-affine McMullen-Bedford c...
• A generalized asymmetric exclusion process with Uq(sl2) stochastic duality AI翻译
  作者：Carinci, Gioia; Giardina, Cristian; Redig, Frank; Sasamoto, Tomohiro
  作者单位：Universita di Modena e Reggio Emilia; Delft University of Technology; Institute of Science Tokyo; Tokyo Institute of Technology
  摘要：We study a new process, which we call ASEP(q, j), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by and where at most particles per site are allowed. The process is constructed from a -dimensional representation of a quantum Hamiltonian with invariance by applying a suitable ground-state transformation. After showing basic properties of the process ASEP(q, j), we prove self-duality with several self-duality functions constructed from the symmetr...
• Asymptotic behaviour of first passage time distributions for Levy processes (vol 157, pg 1, 2013) AI翻译
  作者：Doney, R. A.; Rivero, V.
  作者单位：University of Manchester
• Limits of random differential equations on manifolds AI翻译
  作者：Li, Xue-Mei
  作者单位：University of Warwick
  摘要：Consider a family of random ordinary differential equations on a manifold driven by vector fields of the form where are vector fields, is a positive number, is a diffusion process taking values in possibly a different manifold, are annihilators of . Under Hormander type conditions on we prove that, as approaches zero, the stochastic processes converge weakly and in the Wasserstein topologies. We describe this limit and give an upper bound for the rate of the convergence.