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作者：[Anonymous]
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作者：Blanca, Antonio; Sinclair, Alistair
作者单位：University of California System; University of California Berkeley
摘要：The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the random-cluster model in the canonical case where the underlying graph is an box in the Cartesian lattice . Our main result is a upper bound for the mixing time at all values of the model parameter p except the critical point , and for all values of the second...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：The transition law of every exchangeable Feller process on the space of countable graphs is determined by a -finite measure on the space of -valued arrays. In discrete time, this characterization gives rise to a construction from an independent, identically distributed sequence of exchangeable random functions. In continuous time, the behavior is enriched by a L,vy-It-Khintchine-type decomposition of the jump measure into mutually singular components that govern global, vertex-level, and edge-...
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作者：Ceillier, Gael; Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：Let X be a stationary process with values in some -finite measured state space , indexed by . Call its natural filtration. In Ceillier (Ann Probab 40(5):1980-2007, 2012), sufficient conditions were given for to be standard when E is finite, and the proof used a coupling of all probabilities on the finite set E. In this paper, we construct a coupling of all laws having a density with regard to , which is much more involved. Then, we provide sufficient conditions for to be standard, generalizing...
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作者：Grama, Ion; Le Page, Emile; Peigne, Marc
摘要：Let g1, g2,... be i. i. d. random matrices in GL (d, R). For any n >= 1 consider the product G(n) = g(n) ... g(1) and the random process G(n)v = g(n) ... g(1)v in R-d starting at point v is an element of R-d \ {0}. It is well known that under appropriate assumptions, the sequence (log ||G(n)v||) (n >= 1) behaves like a sum of i. i. d. r. v.' s and satisfies standard classical properties such as the law of large numbers, the law of iterated logarithm and the central limit theorem. For any vecto...
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作者：Hoffman, Christopher; Rizzolo, Douglas; Slivken, Erik
作者单位：University of Washington; University of Washington Seattle; University of Delaware; University of California System; University of California Davis
摘要：Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study fixed points of both 123- and 231-avoiding permutations. We find an exact description for a scaling limit of the empirical distribution of fixed points in terms of Brownian excursion. This builds on the connections between pattern-avoiding permutations and Brownian excursion developed in Hoff...
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作者：Hutchcroft, Tom; Nachmias, Asaf
作者单位：University of British Columbia; Tel Aviv University
摘要：We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible to distinguish the connected components of the forest from each other by invariantly defined graph properties almost surely. This confirms a conjecture of Benjamini et al. (Ann Probab 29(1):1-65, 2001). We also answer positively two additional questions of Benjamini et al. (Ann Probab 29(1):1-65, 2001) under the assu...
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作者：Amini, Omid; Devroye, Luc; Griffiths, Simon; Olver, Neil
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); McGill University; University of Oxford; Vrije Universiteit Amsterdam; Centrum Wiskunde & Informatica (CWI)
摘要：Let T be an infinite rooted tree with weights assigned to its edges. Denote by the minimum weight of a path from the root to a node of the nth generation. We consider the possible behaviour of with focus on the two following cases: we say T is explosive if lim(n ->infinity) m(n)(T) < infinity, and say that T exhibits linear growth if lim inf(n -> 8) m(n)(T)/n > 0. We consider a class of infinite randomly weighted trees related to the Poisson-weighted infinite tree, and determine precisely whic...
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作者：Mendelson, Shahar
作者单位：Technion Israel Institute of Technology
摘要：We introduce an alternative to the notion of 'fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot always be attained by a learning procedure (i.e., a procedure that selects a function in the given class), we introduce an aggregation procedure that attains that rate under rather minimal assumptions-for example, that the and norms are equivalent on the linear...
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作者：Broutin, Nicolas; Marckert, Jean-Francois
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux
摘要：We revisit the discrete additive and multiplicative coalescents, starting with n particles with unit mass. These cases are known to be related to some combinatorial coalescent processes: a time reversal of a fragmentation of Cayley trees or a parking scheme in the additive case, and the random graph process in the multiplicative case. Time being fixed, encoding these combinatorial objects in real-valued processes indexed by the line is the key to describing the asymptotic behaviour of the mass...
