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作者：Klenke, Achim; Mytnik, Leonid
作者单位：Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：We construct a mutually catalytic branching process on a countable site space with infinite branching rate. The finite rate mutually catalytic model, in which the rate of branching of one population at a site is proportional to the mass of the other population at that site, was introduced by Dawson and Perkins (Ann Probab 26(3):1088-1138, 1998). We show that our model is the limit for a class of models and in particular for the Dawson-Perkins model as the rate of branching goes to infinity. Ou...
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作者：Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We prove that probability laws of certain multidimensional semimartingales which includes time-inhomogenous diffusions, under suitable assumptions, satisfy quadratic transportation cost inequality under the uniform metric. From this we derive concentration properties of Lipschitz functions of process paths that depend on the entire history. In particular, we estimate concentration of boundary local time of reflected Brownian motions on a polyhedral domain. We work out explicit applications of ...
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作者：Gravner, Janko; Holroyd, Alexander E.; Morris, Robert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of California System; University of California Davis; Microsoft; University of British Columbia
摘要：Two-dimensional bootstrap percolation is a cellular automaton in which sites become 'infected' by contact with two or more already infected nearest neighbours. We consider these dynamics, which can be interpreted as a monotone version of the Ising model, on an n x n square, with sites initially infected independently with probability p. The critical probability p (c) is the smallest p for which the probability that the entire square is eventually infected exceeds 1/2. Holroyd determined the sh...
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作者：Beltran, J.; Landim, C.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Pontificia Universidad Catolica del Peru; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let r : S x S -> R+ be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m. For alpha > 1, let g : N -> R+ be given by g(0) = 0, g(1) = 1, g(k) = (k/k - 1)(alpha), k >= 2. Consider a zero range process on S in which a particle jumps from a site x, occupied by k particles, to a site y at rate g(k)r(x, y). Let N stand for the total number of particles. In the stationary state, as N up arrow infinity, all particles but a finite num...
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作者：Raimond, Olivier; Schapira, Bruno
作者单位：Universite Paris Saclay; Universite Paris Saclay; Universite Paris Nanterre
摘要：We obtain the convergence in law of a sequence of excited (also called cookies) random walks toward an excited Brownian motion. This last process is a continuous semi-martingale whose drift is a function, say phi, of its local time. It was introduced by Norris, Rogers and Williams as a simplified version of Brownian polymers, and then recently further studied by the authors. To get our results we need to renormalize together the sequence of cookies, the time and the space in a convenient way. ...
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作者：Forrester, Peter J.; Mays, Anthony
作者单位：University of Melbourne
摘要：The generalised eigenvalues for a pair of N x N matrices (X (1), X (2)) are defined as the solutions of the equation det (X (1) - lambda X (2)) = 0, or equivalently, for X (2) invertible, as the eigenvalues of . We consider Gaussian real matrices X (1), X (2), for which the generalised eigenvalues have the rotational invariance of the half-sphere, or after a fractional linear transformation, the rotational invariance of the unit disk. In these latter variables we calculate the joint eigenvalue...
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作者：Horvath, Illes; Toth, Balint; Veto, Balint
作者单位：Budapest University of Technology & Economics
摘要：The problems considered in the present paper have their roots in two different cultures. The `true' (or myopic) self-avoiding walk model (TSAW) was introduced in the physics literature by Amit et al. (Phys Rev B 27:1635-1645, 1983). This is a nearest neighbor non-Markovian random walk in which prefers to jump to those neighbors which were less visited in the past. The self-repelling Brownian polymer model (SRBP), initiated in the probabilistic literature by Durrett and Rogers (Probab Theory Re...
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作者：Nechita, Ion; Pellegrini, Clement
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Kwazulu Natal; University of Kwazulu Natal
摘要：We consider a generalized model of repeated quantum interactions, where a system H is interacting in a random way with a sequence of independent quantum systems K-n, n >= 1. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between H and Kn. The other involves random quantum states describing each copy K-n. In the limit of a large number of interactions, we present convergence results for the asymptotic state o...
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作者：Bakry, Dominique; Bolley, Francois; Gentil, Ivan
作者单位：Universite PSL; Universite Paris-Dauphine; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties of Markov kernels, such as trace estimates. They imply classical bounds on the Ornstein-Uhlenbeck semigroup and a dimensional and refined (transportation) Talagrand inequality when applied to the Hamilton-Jacobi equation. Hypercontractive bounds on the Ornstein-Uhlenbeck semigroup driven by a non-di...
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作者：Nutz, Marcel
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential and logarithmic utility. To derive these results, we combine approaches from optimal control, convex a...
