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- W2897711399 abstract "Abstract Under the assumption that sequences of graphs equipped with resistances, associated measures, walks and local times converge in a suitable Gromov-Hausdorff topology, we establish asymptotic bounds on the distribution of the $varepsilon$ -blanket times of the random walks in the sequence. The precise nature of these bounds ensures convergence of the $varepsilon$ -blanket times of the random walks if the $varepsilon$ -blanket time of the limiting diffusion is continuous at $varepsilon$ with probability 1. This result enables us to prove annealed convergence in various examples of critical random graphs, including critical Galton-Watson trees and the Erdős-Rényi random graph in the critical window. We highlight that proving continuity of the $varepsilon$ -blanket time of the limiting diffusion relies on the scale invariance of a finite measure that gives rise to realizations of the limiting compact random metric space, and therefore we expect our results to hold for other examples of random graphs with a similar scale invariance property." @default.
- W2897711399 created "2018-10-26" @default.
- W2897711399 creator A5043811334 @default.
- W2897711399 date "2023-01-09" @default.
- W2897711399 modified "2023-10-18" @default.
- W2897711399 title "Convergence of blanket times for sequences of random walks on critical random graphs" @default.
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- W2897711399 doi "https://doi.org/10.1017/s0963548322000359" @default.
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