Projects per year
Abstract
We study random walk among random conductance (RWRC) on complete graphs with n vertices. The conductances are i.i.d. and the sum of conductances emanating from a single vertex asymptotically has an infinitely divisible distribution corresponding to a Lévy subordinator with infinite mass at 0. We show that, under suitable conditions, the empirical spectral distribution of the random transition matrix associated to the RWRC converges weakly, as n→∞, to a symmetric deterministic measure on [−1,1], in probability with respect to the randomness of the conductances. In short time scales, the limiting underlying graph of the RWRC is a Poisson Weighted Infinite Tree, and we analyze the RWRC on this limiting tree. In particular, we show that the transient RWRC exhibits a phase transition in which it has positive or weakly zero speed when the mean of the largest conductance is finite or infinite, respectively.
Original language  English 

Pages (fromto)  34773498 
Number of pages  22 
Journal  Stochastic Processes and their Applications 
Volume  130 
Issue number  6 
DOIs  
Publication status  Published  Jun 2020 
Keywords
 Empirical spectral distribution
 Poisson weighted infinite tree
 Random conductance model
 Rate of escape
 Speed
Projects
 1 Finished

Finite Markov chains in statistical mechanics and combinatorics
Garoni, T., Collevecchio, A. & Markowsky, G.
Australian Research Council (ARC)
2/01/14 → 31/12/17
Project: Research