Homogeneous diffusions on the Sierpinski gasket
Homogeneous extensions of random measures
Homogeneous potentials
Homogeneous random measures and strongly supermedian kernels of a Markov process.
Homogenization and ergodic theory
Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach
In this paper, a singular semi-linear parabolic PDE with locally periodic coefficients is homogenized. We substantially weaken previous assumptions on the coefficients. In particular, we prove new ergodic theorems. We show that in such a weak setting on the coefficients, the proper statement of the homogenization property concerns viscosity solutions, though we need a bounded Lipschitz terminal condition.
Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by...
Homogenization of random walk in asymmetric random environment.
Homogenization of semilinear PDEs with discontinuous averaged coefficients.
Homogenization results for a linear dynamics in random Glauber type environment
We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to depend on the random field only by its statistics. The diffusion coefficient defined through the Green–Kubo formula is also studied and its convergence to some homogenized diffusion coefficient is proved.
Homomorphisms for Distributive Operations in Partial Algebras. Applications to Linear Operators and Measure Theory.
Homomorphisms to constructed from random walks
We give a construction of homomorphisms from a group into the reals using random walks on the group. The construction is an alternative to an earlier construction that works in more general situations. Applications include an estimate on the drift of random walks on groups of subexponential growth admitting no nontrivial homomorphism to the integers and inequalities between the asymptotic drift and the asymptotic entropy. Some of the entropy estimates obtained have applications independent of the...
Homotopy and Homology Vanishing Theorems and the Stability of Stochastic Flows.
Horizontal martingales in vector bundles
Horocyclic products of trees
Let be homogeneous trees with degrees , respectively. For each tree, let be the Busemann function with respect to a fixed boundary point (end). Its level sets are the horocycles. The horocyclic product of is the graph consisting of all -tuples with , equipped with a natural neighbourhood relation. In the present paper, we explore the geometric, algebraic, analytic and probabilistic properties of these graphs and their isometry groups. If and then we obtain a Cayley graph of the...
How a centred random walk on the affine group goes to infinity
How does a reflected one-dimensional diffusion bounce back?
How frequently is a system of 2-linear Boolean equations solvable?
How long does it take a transient Bessel process to reach its future infimum?
How many intervals cover a point in random dyadic covering?