• Corpus ID: 245986489

Localization of a one-dimensional simple random walk among power-law renewal obstacles

@inproceedings{Poisat2022LocalizationOA,
  title={Localization of a one-dimensional simple random walk among power-law renewal obstacles},
  author={Julien Poisat and François Simenhaus},
  year={2022}
}
We consider a one-dimensional simple random walk killed by quenched soft obstacles. The position of the obstacles is drawn according to a renewal process with a power-law increment distribution. In a previous work, we computed the large-time asymptotics of the quenched survival probability. In the present work we continue our study by describing the behaviour of the random walk conditioned to survive. We prove that with large probability, the walk quickly reaches a unique time-dependent optimal… 

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References

SHOWING 1-10 OF 50 REFERENCES

A limit theorem for the survival probability of a simple random walk among power-law renewal obstacles

We consider a one-dimensional simple random walk surviving among a field of static soft traps : each time it meets a trap the walk is killed with probability 1−e −β , where β is a positive and fixed

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

Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. For $d \geq 2$ and

Poly-logarithmic localization for random walks among random obstacles

Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$, and run a simple random walk until hitting one of the obstacles. For $d\geq 2$ and $p$ strictly above the

Enlargement of Obstacles for the Simple Random Walk

We consider a continuous time simple random walk moving among obstacles, which are sites (resp., bonds) of the lattice Z d . We derive in this context a version of the technique of enlargement of

Directed polymers in a random environment with heavy tails

We study the model of directed polymers in a random environment in 1 + 1 dimensions, where the distribution at a site has a tail that decays regularly polynomially with power α, where α ∈ (0,2).

SCALING LIMIT FOR TRAP MODELS ON

We give the " quenched " scaling limit of Bouchaud's trap model in d ≥ 2. This scaling limit is the fractional-kinetics process, that is the time change of a d-dimensional Brownian motion by the

Localization for Random Walks Among Random Obstacles in a Single Euclidean Ball

Place an obstacle with probability $$1-p$$ 1 - p independently at each vertex of $${\mathbb {Z}}^d$$ Z d , and run a simple random walk before hitting one of the obstacles. For $$d\ge 2$$ d ≥ 2 and p

The discrete-time parabolic Anderson model with heavy-tailed potential

We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed (1 + d)-dimensional polymer interacting with a random potential, which is constant

Interacting partially directed self-avoiding walk: a probabilistic perspective

We review some recent results obtained in the framework of the 2D interacting self-avoiding walk (ISAW). After a brief presentation of the rigorous results that have been obtained so far for ISAW we

The Parabolic Anderson Model

This is a survey on the intermittent behavior of the parabolic Anderson model, which is the Cauchy problem for the heat equation with random potential on the lattice ℤd. We first introduce the model