Géométrie stochastique sans larmes, I
Geometry of Lipschitz percolation
We prove several facts concerning Lipschitz percolation, including the following. The critical probability pL for the existence of an open Lipschitz surface in site percolation on ℤd with d ≥ 2 satisfies the improved bound pL ≤ 1 − 1/[8(d − 1)]. Whenever p > pL, the height of the lowest Lipschitz surface above the origin has an exponentially decaying tail. For p sufficiently close to 1, the connected regions of ℤd−1 above which the surface has height 2 or more exhibit stretched-exponential...
Geometry of stochastic delay differential equations.
Geometry on the space of positive functions.
Germ-field Markov property for multiparameter processes
systems with resident server and generally distributed arrival and service groups.
Giant component and vacant set for random walk on a discrete torus
We consider random walk on a discrete torus of side-length , in sufficiently high dimension . We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk up to time . We show that when is chosen small, as tends to infinity, there is with overwhelming probability a unique connected component in the vacant set which contains segments of length const . Moreover, this connected component occupies a non-degenerate...
Giant vacant component left by a random walk in a random d-regular graph
We study the trajectory of a simple random walk on a d-regular graph with d ≥ 3 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time un, where u > 0 is a fixed positive parameter. We show that this so-called vacant set exhibits a phase transition in u in the following sense: there...
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...
Gibbsian fields associated to exponentially decreasing quadratic potentials
Gibbs–non-Gibbs properties for evolving Ising models on trees
In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the free-boundary-condition Gibbs state) behaves differently from the plus and the minus state. E.g. at large times, all configurations are bad for the intermediate state, whereas the plus configuration never is bad for the plus state. Moreover, we show that for each...
GI/M/1 queueing systems with service rates depending on the length of queue
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
Glauber dynamics on nonamenable graphs: boundary conditions and mixing time.
Gleason Parts and a Problem in Prediction Theory.
Gleichmäßige Verteilung von Punkten in gewissen metrischen Räumen, speziell auf der Kugel.
Gleichverteilung auf diskreten Halbgruppen.