# Limit theorems for L\'evy flights on a 1D L\'evy random medium

@article{Stivanello2020LimitTF, title={Limit theorems for L\'evy flights on a 1D L\'evy random medium}, author={S. Stivanello and G. Bet and Alessandra Bianchi and M. Lenci and Elena Magnanini}, journal={arXiv: Probability}, year={2020} }

We study a random walk on a point process given by an ordered array of points $(\omega_k, \, k \in \mathbb{Z})$ on the real line. The distances $\omega_{k+1} - \omega_k$ are i.i.d. random variables in the domain of attraction of a $\beta$-stable law, with $\beta \in (0,1) \cup (1,2)$. The random walk has i.i.d. jumps such that the transition probabilities between $\omega_k$ and $\omega_\ell$ depend on $\ell-k$ and are given by the distribution of a $\mathbb{Z}$-valued random variable in the… Expand

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