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作者：Watanabe, Toshiro
作者单位：University of Aizu
摘要：We show that the class of convolution equivalent distributions and the class of locally subexponential distributions are not closed under convolution roots. It gives a negative answer to the classical conjectures of Embrechts and Goldie. Moreover, we establish two sufficient conditions in order that the class of convolution equivalent distributions is closed under convolution roots.
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作者：Backhausz, Agnes; Szegedy, Balazs
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Eotvos Lorand University
摘要：Let d >= 3 be fixed and G be a large random d-regular graph on n vertices. We show that if n is large enough then the entry distribution of every almost eigenvector of G(with entry sum 0 and normalized to have length root n) is close to some Gaussian distribution N(0, sigma) in the weak topology where 0 <= sigma <= 1. Our theorem holds even in the stronger sense when many entries are looked at simultaneously in small random neighborhoods of the graph. Furthermore, we also get the Gaussianity o...
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作者：Asselah, Amine; Schapira, Bruno; Sousi, Perla
作者单位：Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge
摘要：We study the scaling limit of the capacity of the range of a random walk on the integer lattice in dimension four. We establish a strong law of large numbers and a central limit theorem with a non-Gaussian limit. The asymptotic behaviour is analogous to that found by Le Gall in '86 [Comm. Math. Phys. 104 (1986) 471-507] for the volume of the range in dimension two.
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作者：Hulley, Hardy; Ruf, Johannes
作者单位：University of Technology Sydney; University of London; London School Economics & Political Science
摘要：The following conditions are necessary and jointly sufficient for an arbitrary cadlag local martingale to be a uniformly integrable martingale: (A) The weak tail of the supremum of its modulus is zero; (B) its jumps at the first-exit times from compact intervals converge to zero in L-1 on the events that those times are finite; and (C) its almost sure limit is an integrable random variable.
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作者：Le Gall, Jean-Francois; Lehericy, Thomas
作者单位：Universite Paris Saclay
摘要：We study geometric properties of the infinite random lattice called the uniform infinite planar quadrangulation or UIPQ. We establish a precise form of a conjecture of Krikun stating that the minimal size of a cycle that separates the ball of radius R centered at the root vertex from infinity grows linearly in R. As a consequence, we derive certain isoperimetric bounds showing that the boundary size of any simply connected set A consisting of a finite union of faces of the UIPQ and containing ...
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作者：Bourguin, Solesne; Campese, Simon; Leonenko, Nikolai; Taqqu, Murad S.
作者单位：Boston University; University of Luxembourg; Cardiff University
摘要：We obtain quantitative four moments theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumption we make on the Pearson distribution is that it admits four moments. These results are obtained by first proving a general carre du champ bound on the distance between laws of random variables in the domain of a Markov diffusion generator and invariant measures of diffusions, which is of independent interest, and making use of the n...
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作者：Sert, Cagri
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Under a Zariski density assumption, we extend the classical theorem of Cramer on large deviations of sums of i.i.d. real random variables to random matrix products.
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作者：Kenyon, Richard; Miller, Jason; Sheffield, Scott; Wilson, David B.
作者单位：Brown University; University of Cambridge; Massachusetts Institute of Technology (MIT); University of Washington; University of Washington Seattle
摘要：We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the peano curve surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a root 4/3-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter kappa = 12 (i.e., SLE12). This result is universal in t...
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作者：Labbe, Cyril; Lacoin, Hubert
作者单位：Universite PSL; Universite Paris-Dauphine; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universite PSL
摘要：We consider the biased card shuffling and the Asymmetric Simple Exclusion Process (ASEP) on the segment. We obtain the asymptotic of their mixing times: our results show that these two continuous-time Markov chains display cutoff. Our analysis combines several ingredients including: a study of the hydrodynamic profile for ASEP, the use of monotonic eigenfunctions, stochastic comparisons and concentration inequalities.
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作者：Chen, Wei-Kuo; Gamarnik, David; Panchenko, Dmitry; Rahman, Mustazee
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Toronto; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We show that in random K-uniform hypergraphs of constant average degree, for even K >= 4, local algorithms defined as factors of i.i.d. can not find nearly maximal cuts, when the average degree is sufficiently large. These algorithms have been used frequently to obtain lower bounds for the max-cut problem on random graphs, but it was not known whether they could be successful in finding nearly maximal cuts. This result follows from the fact that the overlap of any two nearly maximal cuts in su...
