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作者：Kontorovich, Leonid (Aryeh); Ramanan, Kavita
作者单位：Weizmann Institute of Science; Carnegie Mellon University
摘要：The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, bounds are obtained oil martingale differences associated with the random sequences, which may be of independent interest. As applications of the main result, concentration inequalities are also derived for inhomogeneous Markov chains and hidden Markov ...
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作者：El-Dakkak, Omar; Peccati, Giovanni
作者单位：Sorbonne Universite
摘要：Let X = (X(1), X(2),...) be a nondeterministic infinite exchangeable sequence with values in {0, 1}. We show that X is Hoeffding decomposable if, and only if, X is either an i.i.d. sequence or a Polya sequence. This completes the results established in Peccati [Ann. Probab. 32 (2004) 1796-1829]. The proof uses several combinatorial implications of the correspondence between Hoeffding decomposability and weak independence. Our results must be compared with previous Characterizations of i.i.d. a...
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作者：Caravenna, Francesco; Deuschel, Jean-Dominique
作者单位：University of Padua; Technical University of Berlin
摘要：We consider a random field phi : {1,..., N} -> R as a model fora linear chain attracted to the defect line phi = 0. that is, the x-axis. The free law of the field is specified by the density exp(-Sigma(i) V(Delta phi(i))) with respect to the Lebesgue measure on R(N), where Delta is the discrete Laplacian and we allow for a very large class of potentials V(.). The interaction with the defect line is introduced by giving the field a reward epsilon >= 0 each time it touches the x-axis. We call th...
