-
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.
-
作者：Bogdan, Krzysztof; Kulczycki, Tadeusz; Kwasnicki, Mateusz
作者单位：Wroclaw University of Science & Technology; Purdue University System; Purdue University
摘要：We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open set D. This yields a unique representation of such functions as integrals against measures on D-c boolean OR {infinity} satisfying an integrability condition. The corresponding Martin boundary of D is a subset of the Euclidean boundary determined by an integral test.
-
作者：Osekowski, Adam
作者单位：University of Warsaw
摘要：In the paper we focus on self-adjoint noncommutative martingales. We provide an extension of the notion of differential subordination, which is due to Burkholder in the commutative case. Then we show that there is a noncommutative analogue of the Burkholder method of proving martingale inequalities, which allows us to establish the weak type (1,1) inequality for differentially subordinated martingales. Moreover, a related sharp maximal weak type (1,1) inequality is proved.
-
作者：Ben Efraim, L.; Lust-Piquard, F.
作者单位：Hebrew University of Jerusalem; Weizmann Institute of Science; CY Cergy Paris Universite
摘要：We prove L-p Poincare inequalities with suitable dimension free constants for functions on the discrete cube {- 1, 1}(n). As well known, such inequalities for p an even integer allow to recover an exponential inequality hence the concentration phenomenon first obtained by Bobkov and Gotze. We also get inequalities between the L-p norms of vertical bar|del f | and del(alpha) f, alpha > 0; moreover L-p spaces may be replaced by more general ones. Similar results hold true, replacing functions on...
-
作者：Cattiaux, P.; Guillin, A.; Malrieu, F.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
摘要：We use here a particle system to prove both a convergence result (with convergence rate) and a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are no more uniformly convex. The proof of convergence is simpler than the one in Carrillo-McCann-Villani (Rev. Mat. Iberoamericana 19:971-1018, 2003; Arch. Rat. Mech. Anal. 179:217-263, 2006). All the results complete former results of Malrieu (Ann. Appl. Probab. 13:540-560, 200...
-
作者：Kolesnikov, Alexander V.
作者单位：Scuola Normale Superiore di Pisa
摘要：Let gamma be a Gaussian measure on a Suslin space X, H be the corresponding Cameron-Martin space and {e (i) } subset of H be an orthonormal basis of H. Suppose that mu (n) = rho (n) center dot gamma is a sequence of probability measures which converges weakly to a probability measure mu = rho center dot gamma Consider a sequence of Dirichlet forms {E-n}, where E-n (f) = integral(x) parallel to del Hf parallel to(2)(H)p(n) d gamma and root p(n) epsilon W-2,W-1(gamma).We prove some sufficient co...
-
作者：Akahori, Jiro; Uenishi, Chihiro; Yano, Kouji
作者单位：Kyoto University; Ritsumeikan University
摘要：In this paper a stochastic equation on compact groups in discrete negative time is studied. The diagonal group action on the extreme points of solutions is proved to be transitive by means of the coupling method. This result is applied to generalize Yor's work which is closely related to Tsirelson's stochastic differential equation and to give criteria for existence of a strong solution and for uniqueness in law.
