What question did this study set out to answer?

Determine whether the asymptotic localization ball for a random walk avoiding quenched Bernoulli obstacles is entirely obstacle-free and characterize its limiting one-time spatial distribution.

January 1, 2021The Annals of ProbabilityOpen Access

Distribution of the random walk conditioned on survival among quenched Bernoulli obstacles

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Authors

JDJian DingPeking University RFRyoki FukushimaTokyo Institute of Technology RSRongfeng SunNational University of Singapore

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Implication

Theoretical analysis reveals obstacle-free localization balls in lattice percolation models, indicating exact limiting spatial distributions.

Key Points

Determine whether the asymptotic localization ball for a random walk avoiding quenched Bernoulli obstacles is entirely obstacle-free and characterize its limiting one-time spatial distribution.
Analyzed a simple symmetric random walk on the d-dimensional integer lattice (d ≥ 2) killed upon hitting Bernoulli obstacles placed with probability 1 - p above the site percolation critical threshold.
Conditioned on environments where the origin resides in an infinite obstacle-free connected component.
Applied obstacle perturbation techniques combined with probability estimates and Dirichlet eigenvalue bounds.
Proved that the localization ball of asymptotic volume d log_{1/p} n contains zero obstacles when conditioned on random walk survival up to time n.
Derived the exact limiting one-time spatial distribution of the surviving random walk within the obstacle-free domain.

Cite This Study

Ding et al. (2021) studied this question.

synapsesocial.com/papers/6a984023378ea914c1faf663 https://doi.org/10.1214/20-aop1450

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Implication

Theoretical analysis reveals obstacle-free localization balls in lattice percolation models, indicating exact limiting spatial distributions.

Distribution of the random walk conditioned on survival among quenched Bernoulli obstacles

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Implication

Key Points

Cite This Study

Distribution of the random walk conditioned on survival among quenched Bernoulli obstacles

Discussion

Member takes

Implication

Key Points

Cite This Study

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