2021

最新文章

• PAGERANK'S BEHAVIOR UNDER DEGREE CORRELATIONS AI翻译
  作者：Olvera-Cravioto, Mariana
  作者单位：University of North Carolina; University of North Carolina Chapel Hill
  摘要：The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric, of the rank of a randomly chosen vertex in graphs generated via either a directed configuration model or an inhomogeneous random digraph. The theorem fully characterizes the limiting distribution by expressing it as a random sum of i.i.d. copies of the attr...
• POLLUTED BOOTSTRAP PERCOLATION IN THREE DIMENSIONS AI翻译
  作者：Gravner, Janko; Holroyd, Alexander E.; Sivakoff, David
  作者单位：University of California System; University of California Davis; University of Bristol; University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
  摘要：In the polluted bootstrap percolation model, vertices of the cubic lattice Z(3) are independently declared initially occupied with probability p or closed with probability q, where p + q <= 1. Under the standard (respectively, modified) bootstrap rule, a vertex becomes occupied at a subsequent step if it is not closed and it has at least 3 occupied neighbors (respectively, an occupied neighbor in each coordinate). We study the final density of occupied vertices as p, q -> 0. We show that this ...
• ON THE LIMITATIONS OF SINGLE-STEP DRIFT AND MINORIZATION IN MARKOV CHAIN CONVERGENCE ANALYSIS AI翻译
  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...
• LARGE DEVIATIONS FOR THE EMPIRICAL MEASURE OF THE ZIG-ZAG PROCESS AI翻译
  作者：Bierkens, Joris; Nyquist, Pierre; Schlottke, Mikola C.
  作者单位：Delft University of Technology; Royal Institute of Technology; Eindhoven University of Technology
  摘要：The zig-zag process is a piecewise deterministic Markov process in position and velocity space. The process can be designed to have an arbitrary Gibbs type marginal probability density for its position coordinate, which makes it suitable for Monte Carlo simulation of continuous probability distributions. An important question in assessing the efficiency of this method is how fast the empirical measure converges to the stationary distribution of the process. In this paper we provide a partial a...
• RANDOMIZED HAMILTONIAN MONTE CARLO AS SCALING LIMIT OF THE BOUNCY PARTICLE SAMPLER AND DIMENSION-FREE CONVERGENCE RATES AI翻译
  作者：Deligiannidis, George; Paulin, Daniel; Bouchard-Cote, Alexandre; Doucet, Arnaud
  作者单位：University of Oxford; University of Edinburgh; University of British Columbia
  摘要：The bouncy particle sampler is a Markov chain Monte Carlo method based on a nonreversible piecewise deterministic Markov process. In this scheme, a particle explores the state space of interest by evolving according to a linear dynamics which is altered by bouncing on the hyperplane perpendicular to the gradient of the negative log-target density at the arrival times of an inhomogeneous poisson process (PP) and by randomly perturbing its velocity at the arrival times of a homogeneous PP. Under...
• DERIVATION OF COUPLED KPZ-BURGERS EQUATION FROM MULTI-SPECIES ZERO-RANGE PROCESSES AI翻译
  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 ...
• ROBUST BOUNDS AND OPTIMIZATION AT THE LARGE DEVIATIONS SCALE FOR QUEUEING MODELS VIA RENYI DIVERGENCE AI翻译
  作者：Atar, Rami; Budhiraja, Amarjit; Dupuis, Paul; Wu, Ruoyu
  作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Brown University; Iowa State University
  摘要：This paper develops tools to obtain robust probabilistic estimates for queueing models at the large deviations (LD) scale. These tools are based on the recently introduced robust Renyi bounds, which provide LD estimates (and more generally risk-sensitive (RS) cost estimates) that hold uniformly over an uncertainty class of models, provided that the class is defined in terms of Renyi divergence with respect to a reference model and that estimates are available for the reference model. One very ...
• DIFFUSION-APPROXIMATION FOR A KINETIC EQUATION WITH PERTURBED VELOCITY REDISTRIBUTION PROCESS AI翻译
  作者：Caillerie, Nils; Vovelle, Julien
  作者单位：Georgetown University; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
  摘要：We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the limit we obtain is a parabolic stochastic partial differential equation on the macroscopic parameter, the density here.
• PRECISE ASYMPTOTICS: ROBUST STOCHASTIC VOLATILITY MODELS AI翻译
  作者：Friz, P. K.; Gassiat, P.; Pigato, P.
  作者单位：Universite PSL; Universite Paris-Dauphine
  摘要：We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of Bayer et al. (Math. Finance 30 (2020) 782-832) In essence, we implement a Laplace method on the space of models (in the sense of Hairer), which generalizes classical works of Azencott and Ben Arous on path space and then Aida, In...
• BREAKING A CHAIN OF INTERACTING BROWNIAN PARTICLES AI翻译
  作者：Aurzada, Frank; Betz, Volker; Lifshits, Mikhail
  作者单位：Technical University of Darmstadt; Saint Petersburg State University
  摘要：We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise linear force, with one end of the chain fixed and the other end pulled away at slow speed, in the limit of slow speed and small Brownian noise. We study the instant when the chain breaks, that is, the distance between two neighbouring particles becomes larger than a certain threshold. There are three different regimes depending on the relation between the speed of pulling and the Brownian noise...