-
作者：Cancrini, N.; Martinelli, F.; Roberto, C.; Toninelli, C.
作者单位：Roma Tre University; University of L'Aquila; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We analyze the density and size dependence of the relaxation time for kinetically constrained spin models (KCSM) intensively studied in the physics literature as simple models sharing some of the features of the glass transition. KCSM are interacting particle systems on Z(d) with Glauber-like dynamics, reversible w.r.t. a simple product i.i.d Bernoulli(p) measure. The essential feature of a KCSM is that the creation/destruction of a particle at a given site can occur only if the current config...
-
作者：Fleischmann, Klaus; Wachtel, Vitali
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Munich
摘要：In this paper, we study the large deviation behavior of sums SZ(n) of i.i.d. random variables X-i, where Z(n) is the nth generation of a supercritical Galton Watson process. We assume the finiteness of the moments EX12 and EZ(1)logZ(1). The underlying interplay of large deviation probabilities of partial sums of the X-i and of lower deviation probabilities of Z is clarified. Here, we heavily use lower deviation probability results on Z we recently published in [7].
-
作者：Gine, Evarist; Nickl, Richard
作者单位：University of Connecticut
摘要：Let Pn* K-hn (x) = n(-1)h(n)(-d) Sigma(n)(i= 1) K (( x - X-i)/h(n)) be the classical kernel density estimator based on a kernel K and n independent random vectors X-i each distributed according to an absolutely continuous law P on R-d. It is shown that the processes f ->root n f d(P-n * K-hn - P), f is an element of F, converge in law in the Banach space l infinity(F), for many interesting classes F of functions or sets, some P- Donsker, some just P- pregaussian. The conditions allow for the c...
-
作者：Fontes, Luiz Renato; Schonmann, Roberto H.
作者单位：University of California System; University of California Los Angeles
摘要：We study the threshold theta >= 2 contact process on a homogeneous tree T-b of degree k = b + 1, with infection parameter lambda >= 0 and started from a product measure with density p. The corresponding mean-field model displays a discontinuous transition at a critical point lambda(MF)(c) (k, theta) and for lambda >= lambda(MF)(c) (k, theta) it survives iff p >= p(c)(MF)(k, theta, lambda), where this critical density satisfies 0 < p(c)(MF)(k,theta,lambda) < 1, lim(lambda ->infinity) p(cMF)(k,t...
-
作者：Chen, Z.-Q.; Fitzsimmons, P. J.; Kuwae, K.; Zhang, T.-S.
作者单位：University of California System; University of California San Diego; University of Washington; University of Washington Seattle; Kumamoto University; University of Manchester
摘要：We present a path-space integral representation of the semigroup associated with the quadratic form obtained by a lower-order perturbation of the L-2-infinitesimal generator L of a general symmetric Markov process. An illuminating concrete example for L is Delta(D)- (-Delta)(s)(D), where D is a bounded Euclidean domain in R-d, s epsilon [ 0, 1], Delta(D) is the Laplace operator in D with zero Dirichlet boundary condition and -(-Delta)(D)(s) is the fractional Laplacian in D with zero exterior c...
-
作者：Andjel, Enrique; Mountford, T. S.
作者单位：Aix-Marseille Universite; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We examine the long-range exclusion process introduced by Spitzer and studied by Liggett and answer some of the open questions raised by Liggett. In particular, we show the existence of equilibria corresponding to bounded dual harmonic functions and that the process can have right-discontinuous paths at strictly positive times. We also show that explosions when they occur, do so at fixed times determined by the initial configuration. Finally, we give an example for which the configuration with...
-
作者：Peres, Yuval; Zeitouni, Ofer
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：Let T be a rooted Galton-Watson tree with offspring distribution {p(k)} that has p(0) = 0, mean m = Sigma kp(k) > 1 and exponential tails. Consider the lambda-biased random walk {X-n}(n >= 0) on T; this is the nearest neighbor random walk which, when at a vertex v with d(v) offspring, moves closer to the root with probability lambda(lambda + d(v)), and moves to each of the offspring with probability 1/(lambda + d(v)). It is known that this walk has an a.s. constant speed v = lim(n)|X-n|/n ( wh...
-
作者：Khoshnevisan, Davar
作者单位：Utah System of Higher Education; University of Utah
摘要：Haggstrom et al. (Ann Inst H Poincare Probab Stat 33(4):497-528, 1997) have introduced a dynamical version of percolation on a graph G. When G is a tree they derived a necessary and sufficient condition for percolation to exist at some time t. In the case that G is a spherically symmetric tree (Peres and Steif in Probab Theory Relat Fields 111(1):141-165, 1998), derived a necessary and sufficient condition for percolation to exist at some time t in a given target set D. The main result of the ...
-
作者：Carbone, Raffaella; Sasso, Emanuela
作者单位：University of Pavia; University of Genoa
摘要：We prove hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup on the entire algebra B(h) of bounded operators on a separable Hilbert space h. We exploit the particular structure of the spectrum together with hypercontractivity of the corresponding birth and death process and a proper decomposition of the domain. Then we deduce a logarithmic Sobolev inequality for the semigroup and gain an elementary estimate of the best constant.
-
作者：Barbe, Ph.; McCormick, W. P.
作者单位：University System of Georgia; University of Georgia; Centre National de la Recherche Scientifique (CNRS)
摘要：We establish some asymptotic expansions for infinite weighted convolutions of distributions having rapidly varying subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs to have a general way to calculate higher order expansions, due to possible cancellations of terms. An algebraic methodology is employed to obtain the results.
