Sample path large deviations principles for Poisson shot noise processes, and applications.
Sample Size, Parameter Rates and Contiguity - The i.n.n.i.d. Case
Scaling limit of the prudent walk.
Scaling limit of the random walk among random traps on ℤd
Attributing a positive value τx to each x∈ℤd, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (τx), often known as “Bouchaud’s trap model.” We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that d≥5. We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof by expressing the random walk as the...
Scaling limits of anisotropic Hastings–Levitov clusters
We consider a variation of the standard Hastings–Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic fluctuations...
Scaling of a random walk on a supercritical contact process
We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the random walk...
Second moment convergence rates for uniform empirical processes.
Second order freeness and fluctuations of random matrices. III: Higher order freeness and free cumulants.
Self Diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion
Self-decomposable probability measures on Banach spaces
Self-interacting diffusions II : convergence in law
Self-normalized large deviations for Markov chains.
Semigroup-theoretical proofs of the central limit theorem and other theorems of analysis.
Semi-martingales and rough paths theory.
Semi-recorrido condicionado (expresión asintótica de la r-esperanza condicionada).
In a probability space (Ω,σ,P), for α ⊂ σ a sub-σ field, in general the best approximation in L∞ by elements of L∞(α) has not a unique solution. For the election between these, we prove the convergence P-almost surely of the conditional r-means, when r → ∞, to one solution, which we call conditional mid-range. This is characterized for each ω ∈ Ω by the mid-range, of one regular conditional distribution Q(ω, ·).
Semi-stable probability measures on
Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays
We generalize a theorem of Shao [Proc. Amer. Math. Soc.123 (1995) 575–582] on the almost-sure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation result in the multidimensional setting. The multiscale statistic under consideration was used recently for the selection of the regularization parameter in a number of statistical algorithms as well as...
Sharp estimates of deviations of the sample mean in many dimensions
Sharp large deviations estimates for simulated annealing algorithms
Sharp large deviations for gaussian quadratic forms with applications