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作者：Bordenave, Charles; Caputo, Pietro
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Roma Tre University
摘要：We consider n x n Hermitian matrices with i.i.d. entries X-ij whose tail probabilities P(vertical bar X-ij vertical bar >= t) behave like e(-at alpha) for some a > 0 and alpha is an element of (0, 2). We establish a large deviation principle for the empirical spectral measure of X/root n with speed n(1+alpha/2) with a good rate function J(mu) that is finite only if mu is of the form mu = mu(sc) boxed plus nu for some probability measure nu on R, where boxed plus denotes the free convolution an...
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作者：Da Prato, Giuseppe; Lunardi, Alessandra
作者单位：Scuola Normale Superiore di Pisa; University of Parma
摘要：We consider an elliptic Kolmogorov equation lambda u - Ku = f in a separable Hilbert space H. The Kolmogorov operator K is associated to an infinite dimensional convex gradient system: dX = (AX - DU (X)) dt + dW (t), where A is a self-adjoint operator in H, and U is a convex lower semicontinuous function. Under mild assumptions we prove that for lambda > 0 and f is an element of L-2(H, v) the weak solution u belongs to the Sobolev space W-2,W-2 (H, v), where v is the log-concave probability me...
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作者：Duplantier, Bertrand; Rhodes, Remi; Sheffield, Scott; Vargas, Vincent
作者单位：Universite Paris Saclay; CEA; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Chemistry (INC); Massachusetts Institute of Technology (MIT)
摘要：In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in all dimensions) to a random measure with full support. We also show that the limiting measure has no atom. In connection with the derivative martingale, we write explicit conjectures about the glassy phase of log-correlated Gaussian potentials and the relation...
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作者：Aidekon, Elie; Shi, Zhan
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the boundary case (in the sense of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609-631] in a one-dimensional supercritical branching random walk, and study the additive martingale (W-n). We prove that, upon the system's survival, n(1/2)W(n) converges in probability, but not almost surely, to a positive limit. The limit is identified as a constant multiple of the almost sure limit, discovered by Biggins and Kyprianou, of the derivative martingale.
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作者：Andjel, E. D.
作者单位：Aix-Marseille Universite
摘要：We study subcritical two-dimensional oriented percolation seen from its rightmost point on the set of infinite configurations which are bounded above. This a Feller process whose state space is not compact and has no invariant measures. We prove that it converges in distribution to a measure which charges only finite configurations.
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作者：Armstrong, Scott N.; Smart, Charles K.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Universite PSL; Universite Paris-Dauphine; Massachusetts Institute of Technology (MIT)
摘要：We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is only assumed to have a finite dth moment, where d is the dimension. In the general stationary-ergodic framework, we show that the equation homogenizes to a deterministic, uniformly elliptic equation, and we obtain an explicit estimate of the effective ellipti...
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作者：Ekren, Ibrahim; Keller, Christian; Touzi, Nizar; Zhang, Jianfeng
作者单位：University of Southern California; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman-Kac formula to non-Markovian case. We shall prove the existence, uniqueness, stability and comparison principle for the viscosity solutions. The key ingredient of our approach is a functional Ito calculus recently introduced by Dupire [Functional Ito calculus (2009...
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作者：Tsirelson, Boris
作者单位：Tel Aviv University
摘要：A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of sigma-fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of sigma-fields. The largest extension of such Boolean algebra of sigma-fields, being well-defined always, is a complete Boolean algebra if and only if the noise is classical, which answers an old question of J. Feldman.
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作者：Jara, M.; Landim, C.; Teixeira, A.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie
摘要：Consider a sequence of possibly random graphs G(N) = (V-N, E-N), N >= 1, whose vertices's have i.i.d. weights {W-x(N) : x is an element of V-N} with a distribution belonging to the basin of attraction of an alpha-stable law, 0 < alpha < 1. Let X-t(N), t >= 0, be a continuous time simple random walk on G(N) which waits a mean W-x(N) exponential time at each vertex x. Under considerably general hypotheses, we prove that in the ergodic time scale this trap model converges in an appropriate topolo...
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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...
