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作者：Fontbona, J.
作者单位：Universidad de Chile; Universidad de Chile; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We develop a McKean-Vlasov interpretation of Navier-Stokes equations with external force field in the whole space, by associating with local mild L(p)-solutions of the 3d-vortex equation a generalized nonlinear diffusion with random space-time birth that probabilistically describes creation of rotation in the fluid due to nonconservativeness of the force. We establish a local well-posedness result for this process and a stochastic representation formula for the vorticity in terms of a vector-w...
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作者：Barlow, Martin T.; Zheng, Xinghua
作者单位：University of British Columbia; Hong Kong University of Science & Technology
摘要：We consider a random walk in an lid. Cauchy-tailed conductances environment. We obtain a quenched functional CLT for the suitably rescaled random walk, and, as a key step in the arguments, we improve the local limit theorem for p(n)(omega)2(t)(0, y) in [Ann. Probab. (2009). To appear], Theorem 5.14, to a result which gives uniform convergence for p(n)(omega)2(t) (x, y) for all x, y in a ball.
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作者：Mischaikow, Konstantin; Wanner, Thomas
作者单位：Rutgers University System; Rutgers University New Brunswick; George Mason University
摘要：Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only through experimental observation or numerical simulations. In both cases, the data on which the topological measurements are based are derived via some form of finite sampling or discretization. In this paper, we present a probabilistic approach to quantifying the...
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作者：Armendariz, Ines
摘要：We introduce a one-dimensional stochastic system where particles perform independent diffusions and interact through pairwise coagulation events, which occur at a nontrivial rate upon collision. Under appropriate conditions on the diffusion coefficients, the coagulation rates and the initial distribution of particles, we derive a spatially inhomogeneous version of the mass flow equation as the particle number tends to infinity. The mass flow equation is in one-to-one correspondence with Smoluc...
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作者：Evans, Steven N.; Sturmfels, Bernd; Uhler, Caroline
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the m-dimensional lattice and for which the in matrices that record the transition probabilities in each of the lattice directions commute pair-wise. One reason such processes are of interest is that the transition matrix is straightforward to diagonalize, and hence it is easy to compute n step transition probabilities. The set of commutin...
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作者：Mohamed, Hanene; Robert, Philippe
作者单位：Universite Paris Saclay; Inria
摘要：In this paper, a general tree algorithm processing a random flow of arrivals is analyzed. Capetanakis-Tsybakov-Mikhailov's protocol in the context of communication networks with random access is an example of such an algorithm. In computer science, this corresponds to a trie structure with a dynamic input. Mathematically, it is related to a stopped branching process with exogeneous arrivals (immigration). Under quite general assumptions on the distribution of the number of arrivals and on the ...
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作者：Bordenave, Charles; Torrisi, Giovanni Luca
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Rome Tor Vergata; Consiglio Nazionale delle Ricerche (CNR); Istituto per le Applicazioni del Calcolo Mauro Picone (IAC-CNR)
摘要：We analyze the asymptotic properties of a Euclidean optimization problem on the plane. Specifically, we consider a network with three bins and n objects spatially uniformly distributed, each object being allocated to a bin at a cost depending on its position. Two allocations are considered: the allocation minimizing the bin loads and the allocation allocating each object to its less costly bin. We analyze the asymptotic properties of these allocations as the number of objects grows to infinity...
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作者：Krieger, Abba M.; Pollak, Moshe; Samuel-Cahn, Ester
作者单位：University of Pennsylvania; Hebrew University of Jerusalem
摘要：The present paper studies the limiting behavior of the average score of a sequentially selected group of items or individuals, the underlying distribution of which, F, belongs to the Gumbel domain of attraction of extreme value distributions. This class contains the Normal, Lognormal, Gamma, Weibull and many other distributions. The selection rules are the better than average (beta = 1) and the beta-better than average rule, defined as follows. After the first item is selected, another item is...
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作者：Kargin, Vladislav
作者单位：Stanford University
摘要：Suppose that X(1), ... , X(n), ... are i.i.d. rotationally invariant N-by-N matrices. Let Pi(n) = X(n) ... X(1). It is known that n(-1) log vertical bar Pi(n)vertical bar converges to a non-random limit. We prove that under certain additional assumptions on matrices X(i) the speed of convergence to this limit does not decrease when the size of matrices, N, grows.
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作者：Barrera, Javiera; Fontbona, Joaquin
作者单位：Universidad Adolfo Ibanez; Universidad de Chile; Universidad de Chile
摘要：We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a law of large numbers for random partitions, a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split a...
