-
作者：Rezakhanlou, Fraydoun
作者单位：University of California System; University of California Berkeley
摘要：The Marcus-Lushnikov process is a simple mean field model of coagulating particles that converges to the homogeneous Smoluchowski equation in the large mass limit. If the coagulation rates grow sufficiently fast as the size of particles get large, giant particles emerge in finite time. This is known as gelation, and such particles are known as gels. Gelation comes in different flavors: simple, instantaneous and complete. In the case of an instantaneous gelation, giant particles are formed in a...
-
作者：Basse-O'Connor, Andreas; Rosinski, Jan
作者单位：Aarhus University; University of Tennessee System; University of Tennessee Knoxville
摘要：Let X-n be independent random elements in the Skorohod space D([0, 1]; E) of cadlag functions taking values in a separable Banach space E. Let S-n = Sigma(n)(j=1) X-j. We show that if Sn converges in finite dimensional distributions to a cadlag process, then S-n + y(n) converges a.s. pathwise uniformly over [0, 1], for some y(n) is an element of D([0, 1]; E). This result extends the Ito-Nisio theorem to the space D([0, 1]; E), which is surprisingly lacking in the literature even for E = R. The...
-
作者：Roberts, Matthew I.
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We give short proofs of two classical results about the position of the extremal particle in a branching Brownian motion, one concerning the median position and another the almost sure behaviour.
-
作者：Srivastava, Nikhil; Vershynin, Roman
作者单位：Institute for Advanced Study - USA; University of Michigan System; University of Michigan
摘要：We study the minimal sample size N = N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound N = O(n) for every distribution whose k-dimensional marginals have uniformly bounded 2 + epsilon moments outside the sphere of radius O(root k). In the specific case of log-concave distributions, this result provides an alternative approach to the Kannan-L...
-
作者：Lawler, Gregory F.; Werness, Brent M.
作者单位：University of Chicago
摘要：In this paper we define and prove of the existence of the multi-point Green's function for SLE a normalized limit of the probability that an SLE kappa curve passes near to a pair of marked points in the interior of a domain. When kappa <8 this probability is nontrivial, and an expression can be written in terms two-sided radial SLE. One of the main components to our proof is a refinement of a bound first provided by Beffara [Ann. Probab. 36 (2008) 14211452]. This work contains a proof of this ...
-
作者：Hazra, Rajat Subhra; Maulik, Krishanu
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：In this article, we introduce the notion of free subexponentiality, which extends the notion of subexponentiality in the classical probability setup to the noncommutative probability spaces under freeness. We show that distributions with regularly varying tails belong to the class of free subexponential distributions. This also shows that the partial sums of free random elements having distributions with regularly varying tails are tail equivalent to their maximum in the sense of Ben Arous and...
-
作者：Reitzner, Matthias; Schulte, Matthias
作者单位：University Osnabruck; Helmholtz Association; Karlsruhe Institute of Technology
摘要：A U-statistic of a Poisson point process is defined as the sum Sigma f(x(1),...,x(k)) over all (possibly infinitely many) k-tuples of distinct points of the point process. Using the Malliavin calculus, the Wiener-Ito chaos expansion of such a functional is computed and used to derive a formula for the variance. Central limit theorems for U-statistics of Poisson point processes are shown, with explicit bounds for the Wasserstein distance to a Gaussian random variable. As applications, the inter...
-
作者：Nourdin, Ivan; Peccati, Giovanni
作者单位：Universite de Lorraine
摘要：We prove that an adequately resealed sequence {F-n} of self-adjoint operators, living inside a fixed free Wigner chaos of even order, converges in distribution to a centered free Poisson random variable with rate lambda > 0 if and only if phi(F-n(4)) - 2 phi(F-n(3)) -> 2 lambda(2) - lambda (where phi is the relevant tracial state). This extends to a free setting some recent limit theorems by Nourdin and Peccati [Ann. Probab. 37 (2009) 1412-1426] and provides a noncentral counterpart to a resul...
-
作者：Dereich, Steffen; Moerters, Peter
作者单位：University of Munster; University of Bath
摘要：We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We give a criterion for the existence of a giant component, which is both necessary and sufficient, and which becomes explicit when f is linear. Otherwise it allows the derivation of explicit necessary and sufficient conditions, which are often fairly close. We ...
-
作者：Bakhtin, Yuri
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove existence and uniqueness of a global solution in a certain class. We describe its basin of attraction that can also be viewed as the main ergodic component for the model. We establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics. We also...
