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作者：Cuny, Christophe
作者单位：Universite Paris Saclay
摘要：We prove that, for (adapted) stationary processes, the so-called Maxwell-Woodroofe condition is sufficient for the law of the iterated logarithm and that it is optimal in some sense. That result actually holds in the context of Banach valued stationary processes, including the case of L-P-valued random variables, with 1 <= p < infinity. In this setting, we also prove the weak invariance principle, hence generalizing a result of Peligrad and Utev [Ann. Probab. 33 (2005) 798-815]. The proofs mak...
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作者：Sapozhnikov, Artem
作者单位：Leipzig University
摘要：For a general class of percolation models with long-range correlations on Zd, d >= 2, introduced in [J. Math. Phys. 55 (2014) 083307], we establish regularity conditions of Barlow [Ann. Probab. 32 (2004) 3024-3084] that mesoscopic subballs of all large enough balls in the unique infinite percolation cluster have regular volume growth and satisfy a weak Poincare inequality. As immediate corollaries, we deduce quenched heat kernel bounds, parabolic Harnack inequality, and finiteness of the dimen...
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作者：Corwin, Ivan; Tsai, Li-Cheng
作者单位：Columbia University; Sorbonne Universite; Stanford University
摘要：We prove that under a particular weak scaling, the 4-parameter interacting particle system introduced by Corwin and Petrov [Comm. Math. Phys. 343 (2016) 651-700] converges to the Kardar-Parisi-Zhang (KPZ) equation. This expands the relatively small number of systems for which weak universality of the KPZ equation has been demonstrated.
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作者：Zhang, Xicheng
作者单位：Wuhan University
摘要：Consider the following nonlocal integro-differential operator: for alpha is an element of (0, 2): L-sigma,b((alpha)) f(x) := p.v. integral(|z| < delta) f(x + sigma(x)z) - f(x)/|z|(d+alpha) dz + b(x) . del f(x) + Lf(x), where sigma :R-d -> R-d circle times R-d and b : R-d -> R-d are smooth functions and have bounded partial derivatives of all orders greater than 1, delta is a small positive number, p.v. stands for the Cauchy principal value and L is a bounded linear operator in Sobolev spaces. ...
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作者：Seppalainen, Timo
作者单位：University of Wisconsin System; University of Wisconsin Madison
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作者：Dereich, Steffen; Doring, Leif; Kyprianou, Andreas E.
作者单位：University of Munster; University of Mannheim; University of Bath
摘要：Since the seminal work of Lamperti, there is a lot of interest in the understanding of the general structure of self-similar Markov processes. Lamperti gave a representation of positive self-similar Markov processes with initial condition strictly larger than 0 which subsequently was extended to zero initial condition. For real self-sinfilar Markov processes (rssMps), there is a generalization of Lamperti's representation giving a one-to-one correspondence between Markov additive processes and...
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作者：Owada, Takashi; Adler, Robert J.
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater than one. A typical example is given by the Betti numbers of Cech complexes built over the cloud. The structure of dependence and sparcity (away from the origin) generated by these distributions leads to limit laws expressible via nonhomogeneous, random, Poisson measures. The parametrisation of the limits depends on...
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作者：Ben-Hamou, Anna; Salez, Justin
作者单位：Universite Paris Cite; Universite Paris Cite
摘要：A finite ergodic Markov chain exhibits cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Discovered in the context of card shuffling (Aldous-Diaconis, 1986), this phenomenon is now believed to be rather typical among fast mixing Markov chains. Yet, establishing it rigorously often requires a challengingly detailed understanding of the underlying chain. Here, we consider nonbacktracking r...
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作者：Basu, Riddhipratim; Hermon, Jonathan; Peres, Yuval
作者单位：Stanford University; University of California System; University of California Berkeley; Microsoft
摘要：A sequence of Markov chains is said to exhibit (total variation) cutoff if the convergence to stationarity in total variation distance is abrupt. We consider reversible lazy chains. We prove a necessary and sufficient condition for the occurrence of the cutoff phenomena in terms of concentration of hitting time of worst (in some sense) sets of stationary measure at least a, for some alpha is an element of(0,1). We also give general bounds on the total variation distance of a reversible chain a...
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作者：Peled, Ron
作者单位：Tel Aviv University
摘要：A homomorphism height function on the d-dimensional torus Z(n)(d) is a function on the vertices of the torus taking integer values and constrained to have adjacent vertices take adjacent integer values. A Lipschitz height function is defined similarly but may also take equal values on adjacent vertices. For each of these models, we consider the uniform distribution over all such functions with predetermined values at some fixed vertices (boundary conditions). Our main result is that in high di...
