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作者：Gubinelli, Massimiliano; Tindel, Samy
作者单位：Universite PSL; Universite Paris-Dauphine; Universite de Lorraine
摘要：We generalize Lyons' rough paths theory in order to give a pathwise meaning to some nonlinear infinite-dimensional evolution equation associated to an analytic semigroup and driven by an irregular noise. As an illustration, we discuss a class of linear and nonlinear 1d SPDEs driven by a space-time Gaussian noise with singular space covariance and Brownian time dependence.
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作者：Cerf, R.; Messikh, R. J.
作者单位：Universite Paris Saclay
摘要：We study the behavior of the two-dimensional Ising model in a finite box at temperatures that are below, but very close to, the critical temperature. In a regime where the temperature approaches the critical point and, simultaneously, the size of the box grows fast enough, we establish a large deviation principle that proves the appearance of a round Wulff crystal.
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作者：Bollobas, Bela; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver
作者单位：University of Cambridge; University of Memphis; Microsoft; University of Oxford
摘要：In this paper we determine the percolation threshold for an arbitrary sequence of dense graphs (G(n)). Let lambda(n) be the largest eigenvalue of the adjacency matrix of G(n), and let G(n)(p(n)) be the random subgraph of G(n) obtained by keeping each edge independently with probability p(n). We show that the appearance of a giant component in G(n)(P-n) has a sharp threshold at p(n) = 1/lambda(n). In fact, we prove much more: if (G(n)) converges to an irreducible limit, then the density of the ...
