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作者：Berard, Jean; Ramirez, Alejandro
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Pontificia Universidad Catolica de Chile
摘要：We study the following microscopic model of infection or epidemic reaction: red and blue particles perform independent nearest-neighbor continuous-time symmetric random walks on the integer lattice Z with jump rates D-R for red particles and D-B for blue particles, the interaction rule being that blue particles turn red upon contact with a red particle. The initial condition consists of i.i.d. Poisson particle numbers at each site, with particles at the left of the origin being red, while part...
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作者：Fyodorov, Y. V.; Khoruzhenko, B. A.; Simm, N. J.
作者单位：University of London; Queen Mary University London
摘要：The goal of this paper is to establish a relation between characteristic polynomials of N x N GUE random matrices H as N ->infinity, and Gaussian processes with logarithmic correlations. We introduce a regularized version of fractional Brownian motion with zero Hurst index, which is a Gaussian process with stationary increments and logarithmic increment structure. Then we prove that this process appears as a limit of D-N(Z) = -log vertical bar det(H - zI) on mesoscopic scales as N -> infinity....
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作者：Kahn, Jonas
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille
摘要：Aldous has introduced a notion of scale-invariant random spatial network (SIRSN) as a mathematical formalization of road networks. Intuitively, those are random processes that assign a route between each pair of points in Euclidean space, while being invariant under rotation, translation, and change of scale, and such that the routes are not too long and mainly lie on main roads. The only known example was somewhat artificial since invariance had to be added using randomization at the end of t...
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作者：Bloemendal, Alex; Virag, Balint
作者单位：Harvard University; University of Toronto
摘要：The top eigenvalues of rank r spiked real Wishart matrices and additively perturbed Gaussian orthogonal ensembles are known to exhibit a phase transition in the large size limit. We show that they have limiting distributions for near-critical perturbations, fully resolving the conjecture of Baik, Ben Arous and Peche [Duke Math. J. (2006) 133 205-235]. The starting point is a new (2r + 1)-diagonal form that is algebraically natural to the problem; for both models it converges to a certain rando...
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作者：Ekren, Ibrahim; Touzi, Nizar; Zhang, Jianfeng
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Institut Polytechnique de Paris; Ecole Polytechnique; University of Southern California
摘要：In our previous paper [Ekren, Touzi and Zhang (2015)], we introduced a notion of viscosity solutions for fully nonlinear path-dependent PDEs, extending the semilinear case of Ekren et al. [Ann. Probab. 42 (2014) 204-236], which satisfies a partial comparison result under standard Lipshitz-type assumptions. The main result of this paper provides a full, well-posedness result under an additional assumption, formulated on some partial differential equation, defined locally by freezing the path. N...
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作者：Cai, Chunhao; Chigansky, Pavel; Kleptsyna, Marina
作者单位：Nankai University; Hebrew University of Jerusalem; Le Mans Universite
摘要：This paper presents a new approach to the analysis of mixed processes X-t = B-t + G(t), t is an element of [0, T] where B-t is a Brownian motion and G(t) is an independent centered Gaussian process. We obtain a new canonical innovation representation of X, using linear filtering theory. When the kernel K(s,t) = partial derivative(2)/partial derivative s partial derivative t EG(t)G(s,) s not equal t has a weak singularity on the diagonal, our results generalize the classical innovation formulas...
