Christophe Gallesco

On large deviations for the cover time of two-dimensional torus

Let

A note on spider walks

\mathcal{T}_n

A criterium for non-uniqueness of

be the cover time of two-dimensional discrete torus

g

\mathbb{Z}^2_n=\mathbb{Z}^2/n\mathbb{Z}^2

measures

. We prove that

Dynamic uniqueness for stochastic chains with unbounded memory

\mathbb{P}[\mathcal{T}_n\leq \frac{4}{\pi}\gamma n^2\ln^2 n]=\exp(-n^{2(1-\sqrt{\gamma})+o(1)})

A Conditional Quenched CLT for Random Walks Among Random Conductances on Z(d)

for

Random walks with unbounded jumps among random conductances II: Conditional quenched CLT

\gamma\in (0,1)

Meeting time of independent random walks in random environment

. One of the main methods used in the proofs is the decoupling of the walkers trace into independent excursions by means of soft local times.

Random walks with unbounded jumps among random conductances I: Uniform quenched CLT

A spider consists of several, say