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作者：Mueller, Carl; Mytnik, Leonid; Perkins, Edwin
作者单位：University of Rochester; Technion Israel Institute of Technology; University of British Columbia
摘要：We study the density X(t, x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0 < X( t, x) <= a) as a down arrow 0 as well as the Hausdorff dimension of the boundary of the support of X(t, .). The answers are in terms of the leading eigenvalue of the Ornstein-Uhlenbeck generator with a particular killing term. This work is motivated in part by questions of pathwise uniqueness for associated stochastic partial differential equations.
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作者：Flandoli, Franco; Gess, Benjamin; Scheutzow, Michael
作者单位：University of Pisa; Max Planck Society; Technical University of Berlin
摘要：We provide sufficient conditions for weak synchronization/stabilization by noise for order-preserving random dynamical systems on Polish spaces. That is, under these conditions we prove the existence of a weak point attractor consisting of a single random point. This generalizes previous results in two directions: First, we do not restrict to Banach spaces, and second, we do not require the partial order to be admissible nor normal. As a second main result and application, we prove weak synchr...
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作者：Balazs, Marton; Nagy, Attila Laszlo
作者单位：University of Bristol; Budapest University of Technology & Economics
摘要：We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively (including zero-range, misanthrope and many other models). The initial condition is a step profile, which in some classical cases of asymmetric models, gives rise to a rarefaction fan scenario. We also point out a model with nonconcave, nonconvex hydrodynamics...
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作者：Jakubowski, Adam; Riedle, Markus
作者单位：Nicolaus Copernicus University; University of London; King's College London
摘要：A cylindrical Levy process does not enjoy a cylindrical version of the semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral for random integrands with respect to cylindrical Levy processes in Hilbert spaces. The space of admissible integrands consists of caglad, adapted stochastic processes with values in the space of Hilbert-Schmidt operators. Neither the integrands nor the int...
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作者：Kozma, Gady; Toth, Balint
作者单位：Weizmann Institute of Science; University of Bristol; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：We prove a central limit theorem under diffusive scaling for the displacement of a random walk on Z(d) in stationary and ergodic doubly stochastic random environment, under the H-1-condition imposed on the drift field. The condition is equivalent to assuming that the stream tensor of the drift field be stationary and square integrable. This improves the best existing result [Fluctuations in Markov Processes-Time Symmetry and Martingale Approximation (2012) Springer], where it is assumed that t...
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作者：Foondun, Mohammud; Liu, Wei; Omaba, Mcsylvester
作者单位：University of Strathclyde; Shanghai Normal University
摘要：We consider fractional stochastic heat equations of the form partial derivative u(t)(x)/partial derivative t = -(-Delta)(alpha/2)u(t)(x) + lambda sigma(u(t)(x))(F) over dot (t, x). Here, (F) over dot denotes the noise term. Under suitable assumptions, we show that the second moment of the solution grows exponentially with time. Since we do not assume that the initial condition is bounded below, this solves an open problem stated in [Probab. Theory Related Fields 152 (2012) 681-701]. Along the ...
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作者：Hough, Bob; Jiang, Yunjiang
作者单位：Stanford University
摘要：We consider an analogue of the Kac random walk on the special orthogonal group SO(N), in which at each step a random rotation is performed in a randomly chosen 2-plane of R-N. We obtain sharp asymptotics for the rate of convergence in total variance distance, establishing a cut-off phenomenon in the large N limit. In the special case where the angle of rotation is deterministic, this confirms a conjecture of Rosenthal [Ann. Probab. 22 (1994) 398-423]. Under mild conditions, we also establish a...
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作者：Budhiraja, Amarjit; Dupuis, Paul; Ganguly, Arnab
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University; University of Louisville
摘要：Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive functionals of a PRM.
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作者：Hachem, Walid; Hardy, Adrien; Najim, Jamal
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Royal Institute of Technology; Universite Gustave-Eiffel; ESIEE Paris; Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components. Under mild conditions for the population matrices, we show that for every generic positive edge of that support, there exists an extremal eigenvalue which converges almost surely toward that edge and fluctuates according to the Tracy-Widom law at the scale N...
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作者：Miller, Jason; Sheffield, Scott
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Given a simply connected planar domain D, distinct points x, y is an element of partial derivative D, and kappa > 0, the Schramm-Loewner evolution SLE kappa is a random continuous non-self-crossing path in (D) over bar from x to y. The SLE kappa (rho(1); rho(2)) processes, defined for rho(1), rho(2) > -2, are in some sense the most natural generalizations of SLE kappa. When kappa <= 4, we prove that the law of the time-reversal of an SLE kappa (rho(1); rho(2)) from x to y is, up to parameteriz...
