A quenched functional central limit theorem for planar random walks in random sceneries

@article{GuillotinPlantard2013AQF,
  title={A quenched functional central limit theorem for planar random walks in random sceneries},
  author={Nadine Guillotin-Plantard and Julien Poisat and Renato Soares dos Santos},
  journal={Electronic Communications in Probability},
  year={2013},
  volume={19},
  pages={1-9}
}
Random walks in random sceneries (RWRS) are simple examples of stochastic processes in disordered media. They were introduced at the end of the 70's by Kesten-Spitzer and Borodin, motivated by the construction of new self-similar processes with stationary increments. Two sources of randomness enter in their definition: a random field $\xi = (\xi(x))_{x \in \mathbb{Z}^d}$ of i.i.d. random variables, which is called the random scenery, and a random walk $S = (S_n)_{n \in \mathbb{N}}$ evolving in… 

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