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作者：Sly, Allan
作者单位：University of California System; University of California Berkeley
摘要：Counter to the general notion that the regular tree is the worst case for decay of correlation between sets and nodes, we produce an example of a multi-spin interacting system which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs.
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作者：Herrmann, Samuel; Imkeller, Peter; Peithmann, Dierk
作者单位：Universite de Lorraine; Humboldt University of Berlin
摘要：We investigate exit times from domains of attraction for the motion of a self-stabilized particle traveling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is the effect of including an ensemble-average attraction in addition to the usual state-dependent drift, where the particle is supposed to be suspended in a large population of identical ones. A Kramers' type law for the particle's exit from the potential's domains of attract...
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作者：van der Hofstad, Remco; Morters, Peter; Sidorova, Nadia
作者单位：Eindhoven University of Technology; University of Bath; University of London; University College London
摘要：We study the parabolic Anderson problem, that is, the heat equation partial derivative(t)u = Delta u + xi u on (0,infinity) x Z(d) with independent identically distributed random potential {xi(Z): Z is an element of Z(d)) and localized initial condition u(0, x) = 1(0)(x). Our interest is in the long-term behavior of the random total mass U(t) = Sigma(z) u (t, z) of the unique nonnegative solution in the case that the distribution of xi(0) is heavy tailed. For this, we study two paradigm cases ...
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作者：Morvai, Gusztav; Weiss, Benjamin
作者单位：MTA-BME Stochastics Research Group; Hebrew University of Jerusalem
摘要：A binary renewal process is a stochastic process {X-n} taking values in {0, 1} where the lengths of the runs of 1's between successive zeros are independent. After observing X-0, X-1, ... , X-n one would like to predict the future behavior, and the problem of universal estimators is to do so without any prior knowledge of the distribution. We prove a variety of results of this type, including universal estimates for the expected time to renewal as well as estimates for the conditional distribu...
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作者：Onatski, Alexei
作者单位：Columbia University
摘要：This paper extends the work of E1 Karoui [Ann. Probab. 35 (2007) 663-714] which finds the Tracy-Widom limit for the largest eigenvalue of a nonsingular p-dimensional complex Wishart matrix WC (Omega(p), n) to the case of several of the largest eigenvalues of the possibly singular (n < p) matrix WC(Omega(p), n). As a byproduct, we extend all results of Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643-1697] to the singular Wishart matrix case. We apply our findings to obtain a 95% confiden...
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作者：Remenik, Daniel
作者单位：Cornell University
摘要：We study a contact process running in a random environment in Z(d) where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by nonblocked sites. We give a partial description of the phase diagram of the process, showing in particular that, depending on the flip rates of the environment. survival of the contact process may or may not be possible for large values of the birth rate. We prove block cond...
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作者：Peccati, Giovanni; Prunster, Igor
作者单位：Sorbonne Universite; University of Turin
摘要：A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results for linear and quadratic functionals of such random hazard rates. In particular, we prove central limit theorems for the cumulative hazard function and for the path-second moment and path-variance of the hazard rate. Our techniques are based on recently established criteria for the weak convergence ...
