-
作者：Dupont, Christophe
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let f be an holomorphic endomorphism of P-k and mu be its measure of maximal entropy. We prove an almost sure invariance principle for the systems (P-k, f, mu). Our class U of observables includes the Holder functions and unbounded ones which present analytic singularities. The proof is based on a geometric construction of a Bernoulli coding map omega : (Sigma, s, nu) -> (P-k, f, mu). We obtain the invariance principle for an observable psi on (P-k, f, mu) by applying Philipp-Stout's theorem f...
-
作者：Chapuy, Guillaume
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：A unicellular map is a map which has only one face. We give a bijection between a dominant subset of rooted unicellular maps of given genus and a set of rooted plane trees with distinguished vertices. The bijection applies as well to the case of labelled unicellular maps, which are related to all rooted maps by Marcus and Schaeffer's bijection. This gives an immediate derivation of the asymptotic number of unicellular maps of given genus, and a simple bijective proof of a formula of Lehman and...
-
作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove Ito's formula for the L (p)-norm of a stochastic W(p)1-valued processes appearing in the theory of SPDEs in divergence form.
-
作者：Birkner, Matthias; Greven, Andreas; den Hollander, Frank
作者单位：University of Munich; University of Erlangen Nuremberg; Leiden University - Excl LUMC; Leiden University
摘要：When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In the present paper we consider the quenched LDP, i.e., we condition on a typical letter sequence. We focus on the case where the renewal process has an algebrai...
-
作者：Mariani, Mauro
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：Large deviations principles for a family of scalar 1 + 1 dimensional conservative stochastic PDEs (viscous conservation laws) are investigated, in the limit of jointly vanishing noise and viscosity. A first large deviations principle is obtained in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. A second order large deviations principle is therefore investigated, however, this can ...
-
作者：Driver, Bruce K.; Gordina, Maria
作者单位：University of California System; University of California San Diego; University of Connecticut
摘要：We introduce a class of non-commutative, complex, infinite-dimensional Heisenberg like Lie groups based on an abstract Wiener space. The holomorphic functions which are also square integrable with respect to a heat kernel measure mu on these groups are studied. In particular, we establish a unitary equivalence between the square integrable holomorphic functions and a certain completion of the universal enveloping algebra of the Lie algebra of this class of groups. Using quasi-invariance of the...
-
作者：Chen, Zhen-Qing; Kim, Panki; Song, Renming
作者单位：Seoul National University (SNU); Seoul National University (SNU); University of Washington; University of Washington Seattle; University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper, we study the precise behavior of the transition density functions of censored (resurrected) alpha-stable-like processes in C-1,C-1 open sets in R-d, where d >= 1 and alpha is an element of (1, 2). We first show that the semigroup of the censored alpha-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored alpha-stable-like processes in C...
-
作者：Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
-
作者：Boutillier, Cedric; de Tiliere, Beatrice
作者单位：Universite Paris Cite; Sorbonne Universite; University of Neuchatel
摘要：We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical Z(2), triangular and honeycomb lattice at the critical temperature. Fisher (J Math Phys 7: 1776-1781, 1966) introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dim...
-
作者：Bollobas, Bela; Riordan, Oliver
作者单位：University of Oxford; University of Cambridge; University of Memphis
