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作者：Bakhtin, Yuri; Pajor-Gyulai, Zsolt
作者单位：New York University
摘要：For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. Using Malliavin calculus tools, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits.
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作者：Tsukuda, Koji
作者单位：University of Tokyo
摘要：The Ewens sampling formula was first introduced in the context of population genetics by Warren John Ewens in 1972, and has appeared in a lot of other scientific fields. There are abundant approximation results associated with the Ewens sampling formula especially when one of the parameters, the sample size n or the mutation parameter theta which denotes the scaled mutation rate, tends to infinity while the other is fixed. By contrast, the case that theta grows with n has been considered in a ...
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作者：Carmona, Philippe; Petrelis, Nicolas
作者单位：Nantes Universite
摘要：In this paper we give a complete characterization of the scaling limit of the critical Interacting Partially Directed Self-Avoiding Walk (IPDSAW) introduced in Zwanzig and Lauritzen [J. Chem. Phys. 48 (1968) 3351]. As the system size L is an element of N diverges, we prove that the set of occupied sites, rescaled horizontally by L-2/3 and vertically by L-1/3 converges in law for the Hausdorff distance toward a nontrivial random set. This limiting set is built with a Brownian motion B condition...
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作者：Conus, Daniel; Jentzen, Arnulf; Kurniawan, Ryan
作者单位：Lehigh University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak convergence rates for numerical approximations of such SEEs have been investigated for about two decades and are far away from being well understood: roughly speaking, no essentially sharp weak convergence rates are known for parabolic SEEs with nonlinear diffusion c...
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作者：De, Anindya; O'Donnell, Ryan; Servedio, Rocco A.
作者单位：Northwestern University; Carnegie Mellon University; Columbia University
摘要：In the (deletion-channel) trace reconstruction problem, there is an unknown n-bit source string x. An algorithm is given access to independent traces of x, where a trace is formed by deleting each bit of x independently with probability delta. The goal of the algorithm is to recover x exactly (with high probability), while minimizing samples (number of traces) and running time. Previously, the best known algorithm for the trace reconstruction problem was due to Holenstein et al. [in Proceeding...
