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作者：Landim, Claudio; Pacheco, Carlos G.; Sethuraman, Sunder; Xue, Jianfei
作者单位：Instituto Politecnico Nacional - Mexico; CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; University of Arizona; University of Missouri System; University of Missouri Columbia
摘要：With the recent developments on nonlinear SPDEs, where smoothing of rough noises is needed, one is naturally led to study interacting particle systems whose macroscopic evolution is described by these equations and which possess an in-built smoothing. In this article, our main results are to derive regularized versions of the ill-posed one-dimensional SPDE partial derivative(t)rho = 1/2 Delta Phi(rho) - 2 del (W'Phi(rho)),where the spatial white noise W' is replaced by a regularization W'epsil...
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作者：Pages, Gilles; Panloup, Fabien
作者单位：Universite Paris Cite; Sorbonne Universite; Universite d'Angers; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we focus on nonasymptotic bounds related to the Euler scheme of an ergodic diffusion with a possibly multiplicative diffusion term (nonconstant diffusion coefficient). More precisely, the objective of this paper is to control the distance of the standard Euler scheme with decreasing step (usually called unadjusted Langevin algorithm in the Monte Carlo literature) to the invariant distribution of such an ergodic diffusion. In an appropriate Lyapunov setting and under uniform elli...
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作者：Tremblay, Nicolas; Barthelme, Simon; Usevich, Konstantin; Amblard, Pierre-Olivier
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
摘要：Determinantal point processes (DPPs) are a class of repulsive point pro-cesses, popular for their relative simplicity. They are traditionally defined via their marginal distributions, but a subset of DPPs called L-ensembles have tractable likelihoods and are thus particularly easy to work with. Indeed, in many applications, DPPs are more naturally defined based on the L-ensemble formulation rather than through the marginal kernel.The fact that not all DPPs are L-ensembles is unfortunate, but t...
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作者：Analytis, Pantelis P.; Gelastopoulos, Alexandros; Stojic, Hrvoje
作者单位：University of Southern Denmark; Pompeu Fabra University
摘要：We study a discrete-time Markov process X-n is an element of R-d for which the distribution of the future increments depends only on the relative ranking of its components (descending order by value). We endow the process with a rich-get-richer assumption and show that, together with a finite second moments assumption, it is enough to guarantee almost sure convergence of X-n/n. We characterize the possible limits if one is free to choose the initial state and we give a condition under which th...
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作者：Dirksen, Sjoerd; Mendelson, Shahar
作者单位：Utrecht University; Australian National University
摘要：We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured ma-trix (a randomly subsampled circulant matrix) and is robust to analog pre -quantization noise as well as to adversarial bit corruptions in the quantization process. Our results imply that quantization is not a statistically expensive procedure in the presence of nontrivial analog noise: recovery requires the same sample size one would have needed ha...
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作者：Hosseini, Bamdad; Johndrow, James E.
作者单位：University of Washington; University of Washington Seattle; University of Pennsylvania
摘要：We study a class of Metropolis-Hastings algorithms for target measures that are absolutely continuous with respect to a large class of non-Gaussian prior measures on Banach spaces. The algorithm is shown to have a spec-tral gap in a Wasserstein-like semimetric weighted by a Lyapunov function. A number of error bounds are given for computationally tractable approxima-tions of the algorithm including bounds on the closeness of Cesaro averages and other pathwise quantities via perturbation theory...
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作者：Quattropani, Matteo; Sau, Federico
作者单位：Leiden University; Leiden University - Excl LUMC; University of Trieste
摘要：We analyze the L1-mixing of a generalization of the averaging process introduced by Aldous (2011). The process takes place on a growing sequence of graphs which we assume to be finite-dimensional, in the sense that the random walk on those geometries satisfies a family of Nash inequalities. As a byproduct of our analysis, we provide a complete picture of the total variation mixing of a discrete dual of the averaging process, which we call binomial splitting process. A single particle of this p...
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作者：Lambert, Gaultier; Paquette, Elliot
作者单位：University of Zurich; McGill University
摘要：We investigate the characteristic polynomials phi N of the Gaussian beta ensemble for general beta > 0 through its transfer matrix recurrence. Our motivation is to obtain a (probabilistic) approximation for phi N in terms of a Gaussian log-correlated field. We distinguish between different types of transfer matrices and analyze completely the hyperbolic part of the recurrence. As a result, we obtain a new coupling between phi N and a Gaussian analytic function with an error which is uniform aw...
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作者：Viveros, Roberto
摘要：In the present work, we investigate the case of directed polymer in a random environment (DPRE), when the increments of the one-dimensional random walk are heavy-tailed with tail-exponent equal to zero (P[|X1| >= n] decays slower than any power of n). This case has not yet been studied in the context of directed polymers and presents key differences with the simple symmetric random walk case and the cases where the increments belong to the domain of attraction of an alpha-stable law, where alp...
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作者：Fukasawa, Masaaki; Ugai, Takuto
作者单位：University of Osaka
摘要：Our study aims to specify the asymptotic error distribution in the dis-cretization of a stochastic Volterra equation with a fractional kernel. It is well known that for a standard stochastic differential equation, the discretization error, normalized with its rate of convergence 1/root n, converges in law to the solution of a certain linear equation. Similar to this, we show that a suitably normalized discretization error of the Volterra equation converges in law to the solution of a certain l...
