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作者：Basse-O'Connor, Andreas; Rosinski, Jan
作者单位：Aarhus University; University of Tennessee System; University of Tennessee Knoxville
摘要：Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment Gaussian process and a Gaussian process of finite variation, see Stricker (ZWahrsch Verw Geb 64(3):303-312, 1983). We consider extensions of this result to non Gaussian infinitely divisible processes. First we show that the class of infinitely divisible semimartingales is so large that the natural analog of Stricker's theorem fails to hold. Th...
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作者：Nickl, Richard; Reiss, Markus; Soehl, Jakob; Trabs, Mathias
作者单位：University of Cambridge; Humboldt University of Berlin
摘要：Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate Levy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting object is a Gaussian process that can be obtained from the composition of a Brownian motion with a covariance operator determined by the Levy measure. The results are applied to derive the asymptotic distribution of natural estimators for the distribution functio...
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作者：Rohde, Steffen; Zhan, Dapeng
作者单位：University of Washington; University of Washington Seattle; Michigan State University
摘要：The backward chordal Schramm-Loewner evolution naturally defines a conformal welding homeomorphism of the real line. We show that this homeomorphism is invariant under the automorphism , and conclude that the associated solution to the welding problem (which is a natural renormalized limit of the finite time Loewner traces) is reversible. The proofs rely on an analysis of the action of analytic circle diffeomorphisms on the space of hulls, and on the coupling techniques of the second author.
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作者：Kenyon, Richard W.; Sun, Nike; Wilson, David B.
作者单位：Brown University; Stanford University; Microsoft
摘要：We study asymptotics of the dimer model on large toric graphs. Let be a weighted -periodic planar graph, and let be a large-index sublattice of . For bipartite we show that the dimer partition function on the quotient has the asymptotic expansion where A is the area of , is the free energy density in the bulk, and is a finite-size correction term depending only on the conformal shape of the domain together with some parity-type information. Assuming a conjectural condition on the zero locus of...
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作者：Balister, Paul; Bollobas, Bela; Smith, Paul
作者单位：University of Memphis
摘要：We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on with initial set . We determine T up to a constant factor with high probability for all p above the critical probability for percolation, and to within a factor for a large range of p.
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作者：Benes, Christian; Lawler, Gregory F.; Viklund, Fredrik
作者单位：City University of New York (CUNY) System; Brooklyn College (CUNY); University of Chicago; Royal Institute of Technology; Uppsala University
摘要：We consider loop-erased random walk (LERW) running between two boundary points of a square grid approximation of a planar simply connected domain. The LERW Green's function is the probability that the LERW passes through a given edge in the domain. We prove that this probability, multiplied by the inverse mesh size to the power 3/4, converges in the lattice size scaling limit to (a constant times) an explicit conformally covariant quantity which coincides with the Green's function. The proof d...
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作者：Benaych-Georges, Florent; Rochet, Jean
作者单位：Universite Paris Cite
摘要：This text is about spiked models of non-Hermitian random matrices. More specifically, we consider matrices of the type , where the rank of stays bounded as the dimension goes to infinity and where the matrix is a non-Hermitian random matrix, satisfying an isotropy hypothesis: its distribution is invariant under the left and right actions of the unitary group. The macroscopic eigenvalue distribution of such matrices is governed by the so called Single Ring Theorem, due to Guionnet, Krishnapur a...
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作者：Mikosch, Thomas; Wintenberger, Olivier
作者单位：University of Copenhagen; Sorbonne Universite
摘要：In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin. We study a variety of such functionals, including large deviations of random walks, their suprema, the ruin functional, and further derive weak limit th...
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作者：Chatterjee, Shirshendu
作者单位：City University of New York (CUNY) System; City College of New York (CUNY)
摘要：We consider a model for heterogeneous gene regulatory networks that is a generalization of the model proposed by Chatterjee and Durrett (Random Struct Algorithms 39(2):228-246, 2011) as an annealed approximation of Kauffmann's (J Theor Biol 22(3):437-467, 1969) random Boolean networks. In this model, genes are represented by the vertices of a random directed graph on n vertices having specified in-degree distribution (resp. joint distribution of in-degree and out-degree), and the expression bi...
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作者：Hough, Bob
作者单位：Stanford University
摘要：We study the random walk on the symmetric group generated by the conjugacy class of cycles of length k. We show that the convergence to uniform measure of this walk has a cut-off in total variation distance after steps, uniformly in as . The analysis follows from a new asymptotic estimation of the characters of the symmetric group evaluated at cycles.
