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作者：Asselah, Amine; Schapira, Bruno; Sousi, Perla
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; University of Cambridge
摘要：We prove a strong law of large numbers for the Newtonian capacity of a Wiener sausage in the critical dimension four, where a logarithmic correction appears in the scaling. The main step of the proof is to obtain precise asymptotics for the expected value of the capacity. This requires a delicate analysis of intersection probabilities between two independent Wiener sausages.
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作者：Lambert, Gaultier; Paquette, Elliot
作者单位：University of Zurich; University System of Ohio; Ohio State University
摘要：We compute the leading asymptotics as N of the maximum of the field QN(q)=log|q-AN|,qC, for any unitarily invariant Hermitian random matrix AN associated to a non-critical real-analytic potential. Hence, we verify the leading order in a conjecture ofFyodorov and Simm (Nonlinearity 29:2837, 2016. arXiv:1503.07110 [math-ph]) formulated for the GUE. The method relies on a classical upper-bound and a more sophisticated lower-bound based on a variant of the second-moment method which exploits the h...
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作者：Gravner, Janko; Holroyd, Alexander E.
作者单位：University of California System; University of California Davis; University of Washington; University of Washington Seattle
摘要：In the polluted bootstrap percolation model, the vertices of a graph are independently declared initially occupied with probability p or closed with probability q. At subsequent steps, a vertex becomes occupied if it is not closed and it has at least r occupied neighbors. On the cubic lattice Z(d) of dimension d >= 3 with threshold r = 2, we prove that the final density of occupied sites converges to 1 as p and q both approach 0, regardless of their relative scaling. Our result partially resol...
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作者：Sur, Pragya; Chen, Yuxin; Candes, Emmanuel J.
作者单位：Stanford University; Princeton University; Stanford University
摘要：Logistic regression is used thousands of times a day to fit data, predict future outcomes, and assess the statistical significance of explanatory variables. When used for the purpose of statistical inference, logistic models produce p-values for the regression coefficients by using an approximation to the distribution of the likelihood-ratio test (LRT). Indeed, Wilks' theorem asserts that whenever we have a fixed number p of variables, twice the log-likelihood ratio (LLR) 2 Lambda is distribut...
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作者：Ben Arous, Gerard; Cabezas, Manuel; Fribergh, Alexander
作者单位：New York University; Pontificia Universidad Catolica de Chile; Universite de Montreal
摘要：We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk in Zd converges to the Brownian motion on the integrated super-Brownian excursion when d>14.
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作者：Furlan, M.; Gubinelli, M.
作者单位：Universite PSL; Universite Paris-Dauphine; University of Bonn; University of Bonn
摘要：We establish the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on a three dimensional periodic domain to the dynamic phi 34 model within the framework of paracontrolled distributions. Our work extends previous results of Hairer and Xu to nonlinearities with a finite amount of smoothness (in particular C9 is enough). We use the Malliavin calculus to perform a partial chaos expansion of the stochastic terms and control their Lp norms in terms of the ...
