Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances

2015/06/06 by Ruojun Huang, Takashi Kumagai, Huang, Ruojun +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1506.02193

12 pages

openalex publication_date 2015/06/06 · arxiv created 2015/10/20 · arxiv updated 2015/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider time-dependent random walks among time-dependent conductances. For discrete time random walks, we show that, unlike the time-independent case, two-sided Gaussian heat kernel estimates are not stable under perturbations. This is proved by giving an example of a ballistic and transient time-dependent random walk on Z among uniformly elliptic time-dependent conductances. For continuous time random walks, we show the instability when the holding times are i.i.d. exp(1), and in contrast, we prove the stability when the holding times change by sites in such a way that the base measure is a uniform measure.

Related

• Gradient estimates of the heat kernel for random walks among time-dependent random conductances
• Random walks among time increasing conductances: heat kernel estimates
• Heat kernel estimates and intrinsic metric for random walks with general\n speed measure under degenerate conductances
• Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities
• Laws of the Iterated Logarithm for random walks on Random Conductance Models