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作者：Glover, Kristoffer; Hulley, Hardy; Peskir, Goran
作者单位：University of Technology Sydney; University of Manchester
摘要：Let X = (X-t)(t >= 0) be a transient diffusion process in (0, infinity) with the diffusion coefficient sigma > 0 and the scale function L such that X-t -> infinity as t -> infinity, let I-t denote its running minimum for t >= 0, and let theta denote the time of its ultimate minimum I infinity. Setting c(i, x) = 1 - 2L(x)/L(i) we show that the stopping time tau(*) = inf{t >= 0 vertical bar X-t >= f(*)(I-t)} minimizes E(vertical bar theta - tau vertical bar - theta) over all stopping times tau o...
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作者：Ahdida, Abdelkoddousse; Alfonsi, Aurelien
作者单位：Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator in order to use composition techniques as did Ninomiya and Victoir [Appl. Math. Finance 15 (2008) 107-121] or Alfonsi [Math. Comp. 79 (2010) 209-237]. Doing so, we have found a remarkable splitting for Wishart processes that enables us to sample exactly Wishart distributions without any restriction on the parameters...
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作者：Pekoez, Erol A.; Roellin, Adrian; Ross, Nathan
作者单位：Boston University; National University of Singapore; University of California System; University of California Berkeley
摘要：We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed points of certain distributional transformations which allows us to obtain rates of convergence using a new variation of Stein's method. Despite the large literature on these models, there is surprisingly little known about the limiting distributions so we al...
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作者：Bloznelis, Mindaugas
作者单位：Vilnius University
摘要：We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129-132]. For sparse graphs with a positive clustering coefficient, we examine statistical dependence between the (local) clustering coefficient and the degree. Our results are mathematically rigorous. They are consistent with the empirical observation of Foudalis et al. [In ...
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作者：Teixeira, Augusto; Tykesson, Johan
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Instituto Nacional de Matematica Pura e Aplicada (IMPA); Weizmann Institute of Science
摘要：We consider the model of random interlacements on transient graphs, which was first introduced by Sznitman [Ann. of Math. (2) (2010) 171 2039-2087] for the special case of Z(d) (with d >= 3). In Sznitman [Ann. of Math. (2) (2010) 171 2039-2087], it was shown that on Z(d): for any intensity u > 0, the interlacement set is almost surely connected. The main result of this paper says that for transient, transitive graphs, the above property holds if and only if the graph is amenable. In particular...
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作者：Fill, James Allen
作者单位：Johns Hopkins University
摘要：Most previous studies of the sorting algorithm QuickSort have used the number of key comparisons as a measure of the cost of executing the algorithm. Here we suppose that the n independent and identically distributed (i.i.d.) keys are each represented as a sequence of symbols from a probabilistic source and that QuickSort operates on individual symbols, and we measure the execution cost as the number of symbol comparisons. Assuming only a mild tameness condition on the source, we show that the...
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作者：Luczak, M. J.; Norris, J. R.
作者单位：University of London; University of Cambridge
摘要：We set out a general procedure which allows the approximation of certain Markov chains by the solutions of differential equations. The chains considered have some components which oscillate rapidly and randomly, while others are close to deterministic. The limiting dynamics are obtained by averaging the drift of the latter with respect to a local equilibrium distribution of the former. Some general estimates are proved under a uniform mixing condition on the fast variable which give explicit e...
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作者：Hughes, Christopher; Najnudel, Joseph; Nikeghbali, Ashkan; Zeindler, Dirk
作者单位：University of York - UK; University of Zurich; University of Bielefeld
摘要：We consider a generalization of the Ewens measure for the symmetric group, calculating moments of the characteristic polynomial and similar multiplicative statistics. In addition, we study the asymptotic behavior of linear statistics (such as the trace of a permutation matrix or of a wreath product) under this new measure.
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作者：Collevecchio, Andrea; Cotar, Codina; LiCalzi, Marco
作者单位：Universita Ca Foscari Venezia; Monash University; Technical University of Munich
摘要：We study a general preferential attachment and Polya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not disconnected, it joins an existing pioneer vertex with probability proportional to a function of the degree of that vertex. This function is allowed to be vertex-dependent, and is called the reinforcement function. We prove that there can be at most three phases ...
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作者：Damron, Michael; Hochman, Michael
作者单位：Princeton University
摘要：We construct an edge-weight distribution for i.i.d. first-passage percolation on Z(2) whose limit shape is not a polygon and whose extreme points are arbitrarily dense in the boundary. Consequently, the associated Richardson-type growth model can support coexistence of a countably infinite number of distinct species, and the graph of infection has infinitely many ends.
