4 problems

A random scenery assigns colors independently to the sites of the lattice, and a single defect means two sceneries that differ at exactly one point. The 2-color detection conjectur…

Kesten–Spitzer conjecture. There exist constants $a_n\to\infty$ such that the normalized random-walk-in-random-scenery process converges weakly to a Brownian motion when…

Let $p\in[\frac12,1]$ and $\varepsilon\in[0,1)$ be the parameters of the random walk, and let $\mathbb{B}$ be the set of bad configurations. A configuration is good when it is not…

Let $\boldsymbol{B}$ denote the set of bad color configurations for the random walk in random scenery, and let $p\in[\frac12,1]$ and $\varepsilon\in[0,1)$ be the walk parameters. T…