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作者：Debussche, Arnaud; Liu, Ruoyuan; Tzvetkov, Nikolay; Visciglia, Nicola
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; University of Edinburgh; University of Edinburgh; Heriot Watt University; Ecole Normale Superieure de Lyon (ENS de LYON); University of Pisa
摘要：We consider the nonlinear Schr & ouml;dinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labb & eacute; (Electron Commun Probab 20(43):11, 2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (Nonlinearity 32(4):1147-11...
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作者：Olesker-Taylor, Sam; Zanetti, Luca
作者单位：University of Warwick; University of Bath
摘要：In the Fastest Mixing Markov Chain problem, we are given a graph G = (V, E) and desire the discrete-time Markov chain with smallest mixing time tau subject to having equilibrium distribution uniform on V and non-zero transition probabilities only across edges of the graph. It is well-known that the mixing time tau(RW) of the lazy random walk on G is characterised by the edge conductance Phi of G via Cheeger's inequality: Phi(-1) less than or similar to tau(RW) less than or similar to Phi(-2) l...
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作者：Cass, Thomas; Ferrucci, Emilio
作者单位：Imperial College London; University of Oxford
摘要：We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with Hurst parameter H is an element of (1/4,1). At level 0, our result yields an expression for the expected signature of such processes, which determines their law (Chevyrev and Lyons in Ann Probab 44(6):4049-4082, 2016). In particular, this formula simultaneously extends both the one for 1/2 < H-fBm (Baudoin and Coutin in Stochast Process Appl 117(5):...
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作者：Vidmar, Matija; Warren, Jon
作者单位：University of Ljubljana; University of Warwick
摘要：The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Being local means, roughly, determined by the local behavior of the sample paths of the Brownian motion, and stationary means invariant relative to the Levy shifts of the sample paths. We answer to the affirmative Tsirelson's question, whether or not there are any others, and develop some general theory for such sets. ...
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作者：Yan, Shuo
作者单位：University System of Maryland; University of Maryland College Park
摘要：We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a diffusion process on the corresponding Reeb graph, with certain gluing conditions specified at the interior vertices, as in the case of additive white noise perturbations of Hamiltonian systems considered by M. Freidlin and A. Wentzell. The current paper provi...
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作者：Moench, Christian
作者单位：Johannes Gutenberg University of Mainz
摘要：We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the tra...
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作者：Narayanan, Hariharan; Sheffield, Scott; Tao, Terence
作者单位：Tata Institute of Fundamental Research (TIFR); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles
摘要：Associated to two given sequences of eigenvalues lambda(1) >= ... >=lambda(n) and mu(1) >= ... = mu(n) is a natural polytope, the polytope of augmented hives with the specified boundary data, which is associated to sums of random Hermitian matrices with these eigenvalues. As a first step towards the asymptotic analysis of random hives, we show that if the eigenvalues are drawn from the GUE ensemble, then the associated augmented hives exhibit concentration as n -> infinity. Our main ingredient...
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作者：Dung, Nguyen Tien
作者单位：Vietnam National University Hanoi (VNU Hanoi) System; Vietnam National University Ho Chi Minh City (VNUHCM) System
摘要：We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive quantitative estimates for the Fisher information distance. To illustrate the applicability of our approach, explicit rates of Fisher information convergence for quadratic forms and the functions of sample means are provided. For the sums of independent random...
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作者：Bovier, Anton; Schertzer, Adrien
作者单位：University of Bonn
摘要：20 years ago, Bovier, Kurkova, and L & ouml;we (Ann Probab 30(2):605-651, 2002) proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model of spin glasses at high temperatures. In this paper we improve their results in two ways. First, we extend the range of temperatures to cover the entire regime where the quenched and annealed free energies are known to coincide. Second, we identify the main source of the fluctuatio...
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作者：Hotz, Thomas; Le, Huiling; Wood, Andrew T. A.
作者单位：Technische Universitat Ilmenau; University of Nottingham; Australian National University
摘要：We prove a central limit theorem (CLT) for the Fr & eacute;chet mean of independent and identically distributed observations in a compact Riemannian manifold assuming that the population Fr & eacute;chet mean is unique. Previous general CLT results in this setting have assumed that the cut locus of the Fr & eacute;chet mean lies outside the support of the population distribution. In this paper we present a CLT under some mild technical conditions on the manifold plus the following assumption o...
