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作者：Buckdahn, Rainer; Li, Juan; Quincampoix, Marc
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bretagne Occidentale; Shandong University
摘要：In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study for such a game the problem of the existence of a value without Isaacs condition. Not surprising, this requires a suitable concept of mixed strategies which, to the authors' best knowledge, was not known in the context of stochastic differential games. For this, we consider nonan...
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作者：Bollobas, Bela; Holmgren, Cecilia; Smith, Paul; Uzzell, Andrew J.
作者单位：University of Cambridge; University of Memphis
摘要：Let r is an element of N. In r-neighbour bootstrap percolation on the vertex set of a graph G, vertices are initially infected independently with some probability p. At each time step, the infected set expands by infecting all uninfected vertices that have at least r infected neighbours. When p is close to 1, we study the distribution of the time at which all vertices become infected. Given t = t (n) = o (log n/ log log n), we prove a sharp threshold result for the probability that percolation...
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作者：Miller, Jason; Sun, Nike; Wilson, David B.
作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Microsoft
摘要：The conformal loop ensemble CLEK is the canonical conformally invariant probability measure on noncrossing loops in a proper simply connected domain in the complex plane. The parameter K varies between 8/3 and 8; CLE8/3 is empty while CLE8 is a single space-filling loop. In this work, we study the geometry of the CLE gasket, the set of points not surrounded by any loop of the CLE. We show that the almost sure Hausdorff dimension of the gasket is bounded from below by 2 (8 K)(3K 8)/(32K) when 4...
