# 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…

## One Citation

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