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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...
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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].
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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...
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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...
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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...
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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.
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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.
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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.
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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...
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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.
