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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...
