 

Joseph G. Conlon
Perturbation theory for random walk in asymmetric random environment


Published: 
October 29, 2005

Keywords: 
pde with random coefficients, homogenization 
Subject: 
35R60, 60H30, 60J60 


Abstract
In this paper the author continues his investigation into the scaling limit of a
partial difference equation on the ddimensional integer lattice Z^{d},
corresponding to a translation invariant random walk perturbed by a random
vector field. In a previous paper he obtained a formula for the effective
diffusion constant. It is shown here that for the nearest neighbor walk in
dimension d≧ 3 this effective diffusion constant is finite to all orders of
perturbation theory. The proof uses Tutte's decomposition theorem for
2connected graphs into 3blocks.


Acknowledgements
This research was partially supported by NSF under grant DMS0138519.


Author information
University of Michigan, Department of Mathematics, Ann Arbor, MI 481091109
conlon@umich.edu

