Heat kernel and Green function estimates on affine buildings of type A_r

2006/12/14 by Anker, Jean-Philippe, Schapira, Bruno, Trojan, Bartosz
#31C35 #33C52 #33E50 #51E24 #60B15 #60J10. Secondary: 31C12 #60J45 #60J50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary: 42C05 #Probability (math.PR)

paper · doi:10.48550/arxiv.math/0612385

Abstract

We obtain a global estimate of the transition density pⁿ(0,x) associated to a nearest neighbor random walk, called here "simple", on affine buildings of type \widetildeA_r. Then we deduce a global estimate of the Green function. This is the analogue of a result on Riemannian symmetric spaces of the noncompact type.

Related

• Heat kernel and Green function estimates on affine buildings
• Sharp estimates for distinguished random walks on affine buildings of type Ar
• Random walk on a building of type A_r and Brownian motion of the Weyl chamber
• Isotropic random walks on affine buildings
• Martin compactifications of affine buildings