Geometric interpretation of half-plane capacity.
Géométrie de la courbe brownienne plane
Géométrie différentielle stochastique, II
Géométrie stochastique sans larmes, I
Germ-field Markov property for multiparameter processes
Gibbs measures in a markovian context and dimension
The main goal is to use Gibbs measures in a markovian matrices context and in a more general context, to compute the Hausdorff dimension of subsets of [0, 1[ and [0, 1[². We introduce a parameter t which could be interpreted within thermodynamic framework as the variable conjugate to energy. In some particular cases we recover the Shannon-McMillan-Breiman and Eggleston theorems. Our proofs are deeply rooted in the properties of non-negative irreducible matrices and large deviations techniques as...
Girsanov and Feynman–Kac type transformations for symmetric Markov processes
Girsanov type formula for a Lie group valued brownian motion
Girsanov’s transformation for SLE processes, intersection exponents and hiding exponents
Glauber dynamics of continuous particle systems
Global geometry under isotropic Brownian flows.
Glücksspiel und Markovketten.
Gradient estimates in parabolic problems with unbounded coefficients
We study, with purely analytic tools, existence, uniqueness and gradient estimates of the solutions to the Neumann problems associated with a second order elliptic operator with unbounded coefficients in spaces of continuous functions in an unbounded open set Ω in .
Gradient flows of the entropy for jump processes
We introduce a new transport distance between probability measures on that is built from a Lévy jump kernel. It is defined via a non-local variant of the Benamou–Brenier formula. We study geometric and topological properties of this distance, in particular we prove existence of geodesics. For translation invariant jump kernels we identify the semigroup generated by the associated non-local operator as the gradient flow of the relative entropy w.r.t. the new distance and show that the entropy is...
Grandes déviations
Grandes déviations, dynamique de populations et phénomènes malthusiens
Grandes déviations pour une famille de processus de Galton-Watson dépendant de l'effectif de la population
Graph fibrations, graph isomorphism, and PageRank
PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the...
Graphes et algorithme de calcul de probabilités stationnaires d'un processus markovien discret
Green functions on self-similar graphs and bounds for the spectrum of the laplacian
Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method for spectral analysis on self-similar graphs.First, for a rather general, axiomatically defined class of self-similar graphs a graph theoretic analogue to the Banach fixed point theorem is proved. The subsequent results hold for a subclass consisting of “symmetrically” self-similar graphs which however is still more general then...