-
作者：Qin, Qian; Hobert, James P.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; State University System of Florida; University of Florida
摘要：Over the last three decades, there has been a considerable effort within the applied probability community to develop techniques for bounding the convergence rates of general state space Markov chains. Most of these results assume the existence of drift and minorization (d&m) conditions. It has often been observed that convergence rate bounds based on single-step d&m tend to be overly conservative, especially in high-dimensional situations. This article builds a framework for studying this phe...
-
作者：Bernardin, C.; Funaki, T.; Sethuraman, S.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Waseda University; University of Arizona
摘要：We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such fields have been studied in systems with a single species, the multi-species setting is much less understood. Among other results, we show that when the system starts from stationary states with a particular property, the scaling limits of the multi-species fluctuation fields, seen in a characteristic ...
-
作者：Champagnat, Nicolas; Meleard, Sylvie; Viet Chi Tran
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilatera...
-
作者：Bhattacharya, Bhaswar B.; Mukherjee, Somabha; Mukherjee, Sumit
作者单位：University of Pennsylvania; Columbia University
摘要：Consider the random quadratic form T-n = Sigma(1 <= u<= n) a(uv)X(u)X(v), where ((a(uv)))1(<= u,v <= n) is a {0, 1}-valued symmetric matrix with zeros on the diagonal, and X-1, X-2,..., X-n are i.i.d. Ber(p(n)), with p(n) is an element of (0, 1). In this paper, we prove various characterization theorems about the limiting distribution of T-n, in the sparse regime, where p(n) -> 0 such that E(T-n) = O(1). The main result is a decomposition theorem showing that distributional limits of Tn is the...
-
作者：Bate, Michael E.; Connor, Stephen B.; Matheau-Raven, Oliver
作者单位：University of York - UK
摘要：We introduce a new type of card shuffle called one-sided transpositions. At each step a card is chosen uniformly from the pack and then transposed with another card chosen uniformly from below it. This defines a random walk on the symmetric group generated by a distribution which is nonconstant on the conjugacy class of transpositions. Nevertheless, we provide an explicit formula for all eigenvalues of the shuffle by demonstrating a useful correspondence between eigenvalues and standard Young ...
-
作者：Kardaras, Constantinos; Robertson, Scott
作者单位：University of London; London School Economics & Political Science; Boston University
摘要：We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region E and instantaneous covariation c are known, and where the assets are stable with an exogenously given limiting density p, in that their occupancy time measures converge to a law governed by p. This latter assumption is motivated by the observed stability of ranked relative market capitalizations for equity markets....
-
作者：Lil, Jia; Zhang, Congshan; Liu, Yunxiao
作者单位：Duke University; University of North Carolina; University of North Carolina Chapel Hill
摘要：We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Holder classes as special cases. The gen...
-
作者：Calka, Pierre; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Lehigh University
摘要：We consider the convex hull of the perturbed point process comprised of n i.i.d. points, each distributed as the sum of a uniform point on the unit sphere Sd-1 and a uniform point in the d-dimensional ball centered at the origin and of radius n(alpha), alpha is an element of (-infinity,infinity). This model, inspired by the smoothed complexity analysis introduced in computational geometry (J. Comput. Geom. 7 (2016) 101-144; J. ACM 51 (2004) 385-463), is a perturbation of the classical random p...
-
作者：Schapira, Bruno
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We continue the investigation of the localization phenomenon for a vertex reinforced random walk on the integer lattice. We provide some partial results towards a full characterization of the weights for which localization on 5 sites occurs with positive probability, and make some conjecture concerning the almost sure behavior.
-
作者：Cao, Sky
作者单位：Stanford University
摘要：For random combinatorial optimization problems, there has been much progress in establishing laws of large numbers and computing limiting constants for the optimal values of various problems. However, there has not been as much success in proving central limit theorems. This paper introduces a method for establishing central limit theorems in the sparse graph setting. It works for problems that display a key property which has been variously called endogeny, long-range independence and replica...
