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作者：Schulte, Matthias; Yukich, J. E.
作者单位：Hamburg University of Technology; Lehigh University
摘要：We employ stabilization methods and second order Poincare inequalities to establish rates of multivariate normal convergence for a large class of vec-tors (H(1) s ,..., H(m) s ), s >= 1, of statistics of marked Poisson processes on Rd, d >= 2, as the intensity parameters tends to infinity. Our results are appli-cable whenever the functionals H(i) s , i is an element of {1, ... , m}, are expressible as sums of exponentially stabilizing score functions satisfying a moment condition. The rates ar...
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作者：Ayyer, Arvind; Sinha, Shubham
作者单位：Indian Institute of Science (IISC) - Bangalore; University of California System; University of California San Diego
摘要：Fix t >= 2. We first give an asymptotic formula for certain sums of the number of t-cores. We then use this result to compute the distribution of the size of the t-core of a uniformly random partition of an integer n. We show that this converges weakly to a gamma distribution after dividing by root n. As a consequence, we find that the size of the t-core is of the order of root n in expectation. We then apply this result to show that the probability that t divides the hook length of a uniforml...
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作者：Bernardin, Cedric; Chetrite, Raphael; Chhaibi, Reda; Najnudel, Joseph; Pellegrini, Clemnt
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We analyze the strong noise limit of one-dimensional stochastic differ-ential equations (SDEs).Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an intriguing behavior. As the noise grows larger, the solutions exhibit locally a collapsing, that is to say, converge to pure jump processes very reminiscent of a metastability phenomenon. But surprisingly the limiting jump process is decorated by a spike process...
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作者：Baer, Michael; Duraj, Jetlir; Wachtel, Vitali
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University of Bielefeld
摘要：Let S (n) be a centered random walk with finite second moment. We con-sider the integrated random walk T (n) = S(0) + S(1) + center dot center dot center dot + S(n). We prove invariance principles for the meander and for the bridge of this process, un-der the condition that the integrated random walk remains positive. Further-more, we prove the functional convergence of its Doob's h-transform to the h-transform of the Kolmogorov diffusion conditioned to stay positive.
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作者：Olesker-taylor, S. A. M.
作者单位：University of Bath
摘要：We establish cutoff for a natural random walk (RW) on the set of per-fect matchings (PMs), based on rewiring. An n-PM is a pairing of 2n ob-jects. The k -PM RW selects k pairs uniformly at random, disassociates the corresponding 2k objects, then chooses a new pairing on these 2k objects uniformly at random. The equilibrium distribution is uniform over all n-PMs. The 2-PM RW was first introduced by Diaconis and Holmes (Proc. Natl. Acad. Sci. USA 95 (1998) 14600-14602; Electron. J. Probab. 7 (20...
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作者：Miller, Luke; Pitters, Helmut H.
作者单位：University of Oxford; University of California System; University of California Berkeley
摘要：We quantify the behaviour at large scales of the beta coalescent Pi = {Pi(t), t >= 0} with parameters a, b > 0. Specifically, we study the rescaled block size spectrum of Pi(t) and of its restriction Pi(n)(t) to {1, ... , n}. Our main result is a law of large numbers type of result if Pi comes down from infinity. In the case of Kingman's coalescent the derivation of this so-called hydrodynamic limit has been known since the work of Smoluchowski (Z. Phys. 17 (1916) 557-585). We extend Smoluchow...
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作者：Nguyen, Nhu; Yin, George
作者单位：University of Rhode Island; University of Connecticut
摘要：This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analy-sis, nonsmooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled sequence of the iterates has a differential inclusion limit. In addition, it is shown for the first time that a centered and scaled sequence of the...
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作者：Wang, Feng-Yu
作者单位：Tianjin University
摘要：The convergence rate in Wasserstein distance is estimated for the em-pirical measures of symmetric semilinear SPDEs. Unlike in the finite -dimensional case that the convergence is of algebraic order in time, in the present situation the convergence is of log order with a power given by eigen-values of the underlying linear operator.
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作者：Banerjee, Sayan; Brown, Brendan
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We describe and analyze a class of positive recurrent reflected Brownian motions (RBMs) in Rd+ for which local statistics converge to equilibrium at a rate independent of the dimension d. Under suitable assumptions on the reflection matrix, drift and diffusivity coefficients, dimension-independent stretched exponential convergence rates are obtained by estimating contrac-tions in an underlying weighted distance between synchronously coupled RBMs. We also study the symmetric Atlas model as a fi...
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作者：Foo, Jasmine; Gunnarsson, Einar Bjarki; Leder, Kevin; Storey, Kathleen
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Minnesota System; University of Minnesota Twin Cities; Lafayette College
摘要：Over 80% of human cancers originate from the epithelium, which covers the outer and inner surfaces of organs and blood vessels. In stratified epithe-lium, the bottom layers are occupied by stem and stem-like cells that contin-ually divide and replenish the upper layers. In this work, we study the spread of premalignant mutant clones and cancer initiation in stratified epithelium, using the biased voter model on stacked two-dimensional lattices. Our main result is an estimate of the propagation...
