-
作者：Chaumont, L.
作者单位：Universite d'Angers
摘要：We show that the law of the overall supremum (X) over bar (t) = sup(s <= t) X-s of a Levy process X, before the deterministic time t is equivalent to the average occupation measure mu(+)(t) (dx) = integral(t)(0))P(X-s is an element of dx) ds, whenever 0 is regular for both open halflines (-infinity, 0) and (0, infinity). In this case, P((X) over bar (t) is an element of dx) is absolutely continuous for some (and hence for all) t > 0 if and only if the resolvent measure of X is absolutely conti...
-
作者：Schreiber, Tomasz; Thaele, Christoph
作者单位：Nicolaus Copernicus University; University Osnabruck
摘要：The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in R-d, which form a rather new, rich and flexible class of random tessellations considered in stochastic geometry. For this purpose, martingale tools are combined with second-order formulas proved earlier to establish limit theorems for STIT tessellations. More precisely, a Gaussian functional central limit theorem for the surface increment process induced a by STIT tessellatio...
-
作者：Miller, Jason
作者单位：Stanford University
摘要：Let X-1, X-2 be independent random walks on Z(n)(d), d >= 3, each starting from the uniform distribution. Initially, each site of Z(n)(d) is unmarked, and, whenever X-i visits such a site, it is set irreversibly to i. The mean of vertical bar A(i)vertical bar, the cardinality of the set A(i) of sites painted by i, once all of Z(n)(d) has been visited, is 1/2n(d) by symmetry. We prove the following conjecture due to Pemantle and Peres: for each d >= 3 there exists a constant alpha(d) such that ...
-
作者：Cont, Rama; Fournie, David-Antoine
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Columbia University
摘要：We develop a nonanticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative admits a suitable extension to the space of square-integrable martingales. This extension defines a weak d...
-
作者：Fresen, Daniel
作者单位：Yale University
摘要：We show that the convex hull of a large i.i.d. sample from an absolutely continuous log-concave distribution approximates a predetermined convex body in the logarithmic Hausdorff distance and in the Banach-Mazur distance. For log-concave distributions that decay super-exponentially, we also have approximation in the Hausdorff distance. These results are multivariate versions of the Gnedenko law of large numbers, which guarantees concentration of the maximum and minimum in the one-dimensional c...
-
作者：Gozlan, N.; Roberto, C.; Samson, P. -M.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We give a characterization of transport-entropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley-Stroock perturbation lemma).
-
作者：Asselah, Amine; Gaudilliere, Alexandre
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider a cluster growth model on Z(d), called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It is known that the asymptotic shape of the cluster is spherical. When dimension is 2 or more, we prove that fluctuations with respect to a sphere are at most a power of the logarithm of its radius in dimension d >= 2. In so doing, we introduce a closely rel...
-
作者：Cheliotis, Dimitris; den Hollander, Frank
作者单位：National & Kapodistrian University of Athens; Leiden University - Excl LUMC; Leiden University
摘要：In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges.. There are two phases, localized and delocaliied, depending on the inverse temperature and on the disorder bias. Using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process [Birkner, Greven and den Hollander, Probab. Theory Related Fields 148 (2010) 403-456], we derive va...
-
作者：Friedli, S.; Ioffe, D.; Velenik, Y.
作者单位：Universidade Federal de Minas Gerais; Technion Israel Institute of Technology; University of Geneva
摘要：We consider the Bernoulli bond percolation process P-p,P-p' on the nearestneighbor edges of Z(d), which are open independently with probability p < p(c), except for those lying on the first coordinate axis, for which this probability is p'. Define xi(p,p') := - lim(n ->infinity) n(-1) log P-p,P-p' (0 <-> -ne(1)) and xi(p) := xi(p,p). We show that there exists p(c)' = p(c)'(p, d) such that xi(p,p)' = xi(p) if p' < p(c)' and xi(p,p)' < xi(p) if p' > p(c)'. Moreover, p(c)'(p, 2) = p(c)'(p, 3) = p...
-
作者：Osada, Hirofumi
作者单位：Kyushu University
摘要：We investigate the construction of diffusions consisting of infinitely numerous Brownian particles moving in R-d and interacting via logarithmic functions (two-dimensional Coulomb potentials). These potentials are very strong and act over a long range in nature. The associated equilibrium states are no longer Gibbs measures. We present general results for the construction of such diffusions and, as applications thereof, construct two typical interacting Brownian motions with logarithmic intera...
