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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.
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作者：Brunel, Victor-Emmanuel
作者单位：Institut Polytechnique de Paris; ENSAE Paris; University of Haifa
摘要：We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in R-d. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension d, unlike the other estimators that have been proposed so far. For d >= 3, our estimator has a better risk than the previous ones, and it is nearly minimax, up to a logarithmic factor. We also propose an estimator which is adaptive with respect to the structure ...
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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...
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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.
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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 ...
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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...
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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...
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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...
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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...
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作者：Delarue, Francois; Diel, Roland
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional stochastic differential equations, the drift of which is a distribution, by means of rough paths theory. Existence and uniqueness are established in the weak sense when the drift reads as the derivative of a -Holder continuous function, . Regularity of the ...
