A weak quasi-Lindelöf property and quasi-fine supports of measures.
Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
We consider transient one-dimensional random walks in a random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of “valleys“ of height . In the quenched setting, we also sharply estimate the distribution of the walk at time .
An asymptotic expansion for the discrete harmonic potential.
An extended generator and Schrödinger equations.
An extension of a boundedness result for singular integral operators
We study some operators originating from classical Littlewood-Paley theory. We consider their modification with respect to our discontinuous setup, where the underlying process is the product of a one-dimensional Brownian motion and a d-dimensional symmetric stable process. Two operators in focus are the G* and area functionals. Using the results obtained in our previous paper, we show that these operators are bounded on . Moreover, we generalize a classical multiplier theorem by weakening its...
Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
Anomalous heat-kernel decay for random walk among bounded random conductances
We consider the nearest-neighbor simple random walk on ℤd, d≥2, driven by a field of bounded random conductances ωxy∈[0, 1]. The conductance law is i.i.d. subject to the condition that the probability of ωxy>0 exceeds the threshold for bond percolation on ℤd. For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the 2n-step return probability . We prove that is bounded by a random constant timesn−d/2 in d=2, 3, while it...
Anticipation cancelled by a Girsanov transformation : a paradox on Wiener space
Appendice à : « Intégral de capacités fortement sous-additives »
Application d'un théorème de Mokobodzki aux opérateurs potentiels dans le cas récurrent
Approximation of arbitrary Dirichlet processes by Markov chains
Asymptotic estimates of the Green functions and transition probabilities for Markov additive processes.
Avoiding-probabilities for Brownian snakes and super-Browian motion.