How Paul Lévy saw Jean Ville and martingales.
How the maximum of gaussian random walks and fields is influenced by changes of the variances.
In this paper we present an analytical proof of the fact that the maximum of gaussian random walks exceeds an arbitrary level b with a probability that is an increasing function of the step variances. An analogous result for stochastic integrals is also obtained.
How To Build a Barricade.
How to combine fast heuristic Markov chain Monte Carlo with slow exact sampling.
How to Distinguish Between Record Types
How to get Central Limit Theorems for global errors of estimates
The asymptotic behavior of global errors of functional estimates plays a key role in hypothesis testing and confidence interval building. Whereas for pointwise errors asymptotic normality often easily follows from standard Central Limit Theorems, global errors asymptotics involve some additional techniques such as strong approximation, martingale theory and Poissonization. We review these techniques in the framework of density estimation from independent identically distributed random variables,...
Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion.
Huge random structures and mean field models for spin glasses.
Hunt processes and analytic potential theory on rigged Hilbert spaces
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst.
Hydrodynamic limit for a particle system with degenerate rates
We study the hydrodynamic limit for some conservative particle systems with degenerate rates, namely with nearest neighbor exchange rates which vanish for certain configurations. These models belong to the class of kinetically constrained lattice gases (KCLG) which have been introduced and intensively studied in physical literature as simple models for the liquid/glass transition. Due to the degeneracy of rates there exist blocked configurations which do not evolve under the dynamics and in general...
Hydrodynamic limit for asymmetric mean zero exclusion processes with speed change
Hydrodynamic limit for perturbation of a hyperbolic equilibrium point in two-component systems
Hydrodynamic limit of a d-dimensional exclusion process with conductances
Fix a polynomial Φ of the form Φ(α) = α + ∑2≤j≤m aj αk=1j with Φ'(1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on , with conductances given by special class of functionsW, is described by the unique weak solution of the non-linear parabolic partial differential equation ∂tρ = ∑d ∂xk ∂Wk Φ(ρ). We also derive some properties of the operator ∑k=1d ...
Hydrodynamic limit of mean zero asymmetric zero range processes in infinite volume
Hydrodynamic limit of zero range processes among random conductances on the supercritical percolation cluster.
Hydrodynamic scaling limit of continuum solid-on-solid model.
Hydrodynamical behavior of symmetric exclusion with slow bonds
We consider the exclusion process in the one-dimensional discrete torus with points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance , with . We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter . If , the hydrodynamic limit is given by the usual heat equation. If , it is given by a parabolic equation involving an operator , where ...
Hydrodynamical limit for asymmetric attractive particle systems on
Hydrodynamical limit for the asymmetric zero-range process