Hitting properties of a random string.
Homogenization and ergodic theory
Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit
In this paper, we consider two-scale limits obtained with increasing homogenization periods, each period being an entire multiple of the previous one. We establish that, up to a measure preserving rearrangement, these two-scale limits form a martingale which is bounded: the rearranged two-scale limits themselves converge both strongly in L2 and almost everywhere when the period tends to +∞. This limit, called the Two-Scale Shuffle limit, contains all the information present in all the two-scale...
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 two randomly weakly connected materials.