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作者：Last, Guenter; Penrose, Mathew D.; Zuyev, Sergei
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath; Chalmers University of Technology; University of Gothenburg
摘要：Consider a Boolean model in R-d with balls of random, bounded radii with distribution F-0, centered at the points of a Poisson process of intensity t > 0. The capacity functional of the infinite cluster Z(infinity) is given by theta(L) (t) = P{Z(infinity) boolean AND L not equal empty set L not equal phi}, defined for each compact L subset of R-d. We prove for any fixed L and F-0 that theta(L) (t) is infinitely differentiable in t, except at the critical value t(c); we give a Margulis-Russo-ty...
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作者：Gravner, Janko; Sivakoff, David
作者单位：University of California System; University of California Davis; University System of Ohio; Ohio State University
摘要：Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic puzzle graph by using connectivity properties of a random people graph on the same set of vertices. We presume the Erdos-Renyi people graph with edge probability p and investigate the probability that the puzzle is solved, that is, that the process eventually produces a single cluster. In some generality, for puzzle graphs with N vertices of degrees about D (in the appropriate sense), this pr...
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：We consider disordered systems of a directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2 + 1), the long-range directed polymer model with Cauchy tails in dimension (1 + 1) and the disordered pinning model with tail exponent 1/2. We show that in a suitable weak disorder and continuum limit, the partition functions of these different models converge to a universal limit: a log-normal random field ...
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作者：Clement, Dombry; Landy, Rabehasaina
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Marie et Louis Pasteur
摘要：A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex analysis and is expressed in terms of the residues of the function 1/(1 - g). Under the assumption that g can be extended into a meromorphic function on the complex plane and some technical conditions, we obtain even an exact expansion of the renewal function. An...
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作者：Bluemmel, Tilmann; Rheinlaender, Thorsten
作者单位：University of Vienna; Technische Universitat Wien
摘要：We construct a large trader model using tools from nonlinear stochastic integration theory and an impact function. It encompasses many well-known models from the literature. In particular, the model allows price changes to depend on the size as well as on the speed and timing of the large trader's transactions. Moreover, a volume impact limit order book can be studied in this framework. Relaxing a condition about existence of a universal martingale measure governing all resulting small trader ...
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作者：Mossel, Elchanan; Roch, Sebastien
作者单位：Massachusetts Institute of Technology (MIT); University of Wisconsin System; University of Wisconsin Madison
摘要：We consider the reconstruction of a phylogeny from multiple genes under the multispecies coalescent. We establish a connection with the sparse signal detection problem, where one seeks to distinguish between a distribution and a mixture of the distribution and a sparse signal. Using this connection, we derive an information-theoretic trade-off between the number of genes, m, needed for an accurate reconstruction and the sequence length, k, of the genes. Specifically, we show that to detect a b...
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作者：Sly, Allan; Zhang, Yumeng
作者单位：Australian National University; University of California System; University of California Berkeley
摘要：The mixing time of the Glauber dynamics for spin systems on trees is closely related to the reconstruction problem. Martinelli, Sinclair and Weitz established this correspondence for a class of spin systems with soft constraints bounding the log-Sobolev constant by a comparison with the block dynamics [ Comm. Math. Phys. 250 (2004) 301-334; Random Structures Algorithms 31 (2007) 134-172]. However, when there are hard constraints, the dynamics inside blocks may be reducible. We introduce a vari...
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作者：Henry-Labordere, Pierre; Tan, Xiaolu; Touzi, Nizar
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：We propose an unbiased Monte 3 estimator for E [g(X-t1,..., X-tn)], where X is a diffusion process defined by a multidimensional stochastic differential equation (SDE). The main idea is to start instead from a well-chosen simulatable SDE whose coefficients are updated at independent exponential times. Such a simulatable process can be viewed as a regime-switching SDE, or as a branching diffusion process with one single living particle at all times. In order to compensate for the change of the ...
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作者：Doering, Leif; Klenke, Achim; Mytnik, Leonid
作者单位：University of Mannheim; Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：For many stochastic diffusion processes with mean field interaction, convergence of the rescaled total mass processes towards a diffusion process is known. Here, we show convergence of the so-called finite system scheme for interacting jump-type processes known as mutually catalytic branching processes with infinite branching rate. Due to the lack of second moments, the rescaling of time is different from the finite rate mutually catalytic case. The limit of rescaled total mass processes is id...
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作者：Hambly, Ben; Ledger, Sean
作者单位：University of Oxford; University of Bristol
摘要：We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes large, the empirical measure of the population converges to the solution of a nonlinear stochastic heat equation with Dirichlet boundary condition. The diffusion coefficients are allowed to have finitely many discontinuities (piecewise Lipschitz) and we prov...
