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作者：Lerouvillois, Vincent; Toninelli, Fabio
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Technische Universitat Wien
摘要：The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. L. Ferrari in (Comm. Math. Phys. 325 (2014) 603-684), is a classical example of (2 + 1)-dimensional random growth model belonging to the so-called Anisotropic KPZ universality class. In (Comm. Pure Appl. Math. 72 (2018) 620-666), a hydrodynamic limit-the convergence of the height profile, after space/time rescaling, to the solution of a deterministic Hamilton-Jacobi PDE with nonconvex Hamiltonian-was proven when...
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作者：Addario-Berry, Louigi; Devroye, Luc; Lugosi, Gabor; Velona, Vasiliki
作者单位：McGill University; McGill University; ICREA; Pompeu Fabra University; Universitat Politecnica de Catalunya
摘要：We study the broadcasting problem when the underlying tree is a random recursive tree. The root of the tree has a random bit value assigned. Every other vertex has the same bit value as its parent with probability 1 - q and the opposite value with probability q, where q is an element of [0, 1]. The broadcasting problem consists in estimating the value of the root bit upon observing the unlabeled tree, together with the bit value associated with every vertex. In a more difficult version of the ...
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作者：Hu, Ying; Shi, Xiaomin; Xu, Zuo Quan
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Shandong University of Finance & Economics; Hong Kong Polytechnic University
摘要：This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and the Markov chain. Using Ito's lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ES-REs). We prove the existence and uniqueness of the two ESREs u...
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作者：Fang, Xiao; Koike, Yuta
作者单位：Chinese University of Hong Kong; University of Tokyo
摘要：We extend Stein's celebrated Wasserstein bound for normal approximation via exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the symmetry of exchangeable pairs to obtain an error bound for smooth test functions. We also obtain a continuous version of the multi-dimensional Wasserstein bound in terms of fourth moments. We apply the main results to multivariate normal approximations to Wishart matrices of size n and degree d, where we obtain the optimal con...
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作者：Baldasso, Rangel; Pereira, Alan; Reis, Guilherme
作者单位：Bar Ilan University; Universidade Federal de Alagoas; Universidade Federal da Bahia
摘要：We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be nonlinear and path dependent. We prove that the sequence of empirical measures of the full trajectories satisfies a large deviation principle with explicit rate function. The minimizer of the rate function is characterized as the path-dependent McKean-Vlasov diffusion associated t...
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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 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. However, results presented herein suggest that d&m may be less useful in the emerging area of convergence complexity analysis, which is the study of how the convergence behavior of Monte Carlo Markov chains scales with sample size, n, and/or number of covariates, p. The problem appears to be that minorization can become a serious liability as dimension in...
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作者：Doebler, Christian; Kasprzak, Mikolaj J.; Peccati, Giovanni
作者单位：Heinrich Heine University Dusseldorf; University of Luxembourg
摘要：We consider sequences of U-processes based on symmetric kernels of a fixed order, that possibly depend on the sample size. Our main contribution is the derivation of a set of analytic sufficient conditions, under which the aforementioned U-processes weakly converge to a linear combination of time-changed independent Brownian motions. In view of the underlying symmetric structure, the involved time-changes and weights remarkably depend only on the order of the U-statistic, and have consequently...
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作者：Dombry, Clement; Tillier, Charles; Wintenberger, Olivier
作者单位：Universite Marie et Louis Pasteur; Universite Paris Saclay; Universite Paris Cite; Sorbonne Universite
摘要：We consider regular variation for marked point processes with independent heavy-tailed marks and prove a single large point heuristic: the limit measure is concentrated on the cone of point measures with one single point. We then investigate successive hidden regular variation removing the cone of point measures with at most k points, k >= 1, and prove a multiple large point phenomenon: the limit measure is concentrated on the cone of point measures with k + 1 points. We show how these results...
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作者：Bhattacharjee, Chinmoy; Schulte, Matthias
作者单位：University of Luxembourg; Hamburg University of Technology
摘要：We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet. We achieve this by proving convergence of the underlying point process of the degrees to a certain Poisson process. Estimating the index of the power-law tail for the typical degree distribution is an important question in statistics. We prove consistency o...
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作者：Coppini, Fabio
作者单位：Universite Paris Cite
摘要：The stochastic Kuramoto model defined on a sequence of graphs is analyzed: the emphasis is posed on the relationship between the mean field limit, the connectivity of the underlying graph and the long time behavior. We give an explicit deterministic condition on the sequence of graphs such that, for any finite time and any initial condition, even dependent on the network, the empirical measure of the system stays close to the solution of the McKean-Vlasov equation associated to the classical m...
