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作者：Pavlov, Ronnie
作者单位：University of British Columbia
摘要：For any two-dimensional nearest neighbor shift of finite type X and any integer n >= 1, one can define the horizontal strip shift H-n (X) to be the set of configurations on Z x {1, ... , n} which do not contain any forbidden pairs of adjacent letters for X. It is always the case that the sequence h(top)(H-n(X))/n of normalized topological entropies of the strip shifts converges to h(toP)(X), the topological entropy of X. In this paper, we combine ergodic theoretic techniques with methods from ...
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作者：Romik, Dan
作者单位：University of California System; University of California Davis
摘要：The arctic circle theorem of Jockusch, Propp, and Shor asserts that uniformly random domino tilings of an Aztec diamond of high order are frozen with asymptotically high probability outside the arctic circle inscribed within the diamond. A similar arctic circle phenomenon has been observed in the limiting behavior of random square Young tableaux. In this paper, we show that random domino tilings of the Aztec diamond are asymptotically related to random square Young tableaux in a more refined s...
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作者：Graf, Siegfried; Luschgy, Harald; Pages, Gilles
作者单位：University of Passau; Universitat Trier; Universite Paris Cite; Sorbonne Universite
摘要：For a large class of absolutely continuous probabilities P it is shown that, for r > 0, for n-optimal L-r (P)-codebooks alpha(n), and any Voronoi partition V-n,V-a with respect to alpha(n) the local probabilities P(V-n,V-a) satisfy P(V-a,V-n) approximate to n(-1) while the local L-r-quantization errors satisfy integral V-n,V-a parallel to x - a parallel to(r) d P (x) approximate to n(-(1+r/d)) as long as the partition sets V-n,V-a intersect a fixed compact set K in the interior of the support ...
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作者：Kern, Peter; Meerschaert, Mark M.; Scheffler, Hans-Peter
作者单位：Heinrich Heine University Dusseldorf; Michigan State University; Universitat Siegen
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作者：Banica, Teodor; Curran, Stephen; Speicher, Roland
作者单位：CY Cergy Paris Universite; University of California System; University of California Los Angeles; Queens University - Canada; Saarland University
摘要：We study sequences of noncommutative random variables which are invariant under quantum transformations coming from an orthogonal quantum group satisfying the easiness condition axiomatized in our previous paper. For 10 easy quantum groups, we obtain de Finetti type theorems characterizing the joint distribution of any infinite quantum invariant sequence. In particular, we give a new and unified proof of the classical results of de Finetti and Freedman for the easy groups S-n, O-n, which is ba...
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作者：Grimmett, Geoffrey R.; Holroyd, Alexander E.
作者单位：University of Cambridge; University of British Columbia; Microsoft
摘要：Does there exist a Lipschitz injection of Z(d) into the open set of a site percolation process on Z(D), if the percolation parameter p is sufficiently close to 1? We prove a negative answer when d = D and also when d >= 2 if the Lipschitz constant M is required to be I. Earlier work of Dirr, Dondl, Grimmett, Holroyd and Scheutzow yields a positive answer for d < D and M = 2. As a result, the above question is answered for all d, D and M. Our proof in the case d = D uses Tucker's lemma from top...
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作者：Bailleul, Ismael; Franchi, Jacques
作者单位：University of Cambridge; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：Some general Lorentz covariant operators, associated to the so-called Theta (or Xi)-relativistic diffusions and making sense in any Lorentzian manifold, have been introduced by Franchi and Le Jan [Comm. Pure Appl. Math. 60 (2007) 187-251], Franchi and Le Jan [Curvature diffusions in general relativity (2010). Unpublished manuscript]. Only a few examples have been studied so far. We provide in this work some nonexplosion criteria for these diffusions, which can be used in generic cases.
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作者：Ceillier, Gael
摘要：Let X be a stationary process with finite state-space A. Bressaud et al. [Ann. Probab. 34 (2006) 1589-1600] recently provided a sufficient condition for the natural filtration of X to be standard when A has size 2. Their condition involves the conditional laws p(.vertical bar x) of X-0 conditionally on the whole past (X-k)(k <=-1) = x and controls the strength of the influence of the old past of the process on its present X-0. It involves the maximal gaps between p(.vertical bar x) and p(.vert...
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作者：Heuser, Aaron
作者单位：National Institutes of Health (NIH) - USA
摘要：This paper examines the existence of the self-intersection local time for a superprocess over a stochastic flow in dimensions d <= 3, which through constructive methods, results in a Tanaka-like representation. The superprocess over a stochastic flow is a superprocess with dependent spatial motion, and thus Dynkin's proof of existence, which requires multiplicity of the log-Laplace functional, no longer applies. Skoulakis and Adler's method of calculating moments is extended to higher moments,...
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作者：Chen, Zhen-Qing; Fitzsimmons, Patrick J.; Kuwae, Kazuhiro; Zhang, Tu-Sheng
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California San Diego; Kumamoto University; University of Manchester
