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Random walks, Kleinian groups, and bifurcation currents
Random walks Kleinian groups bifurcation currents
2010/11/11
Let (\rho_\lambda)_{\lambda\in \Lambda} be a holomorphic family of representations of a finitely generated group G into PSL(2,C), parameterized by a complex manifold \Lambda . We define a notion of b...
Upper tails of self-intersection local times of random walks: survey of proof techniques
self-intersection random walks
2010/11/19
The asymptotics of the probability that the self-intersection local time of a random walk on $\Z^d$ exceeds its expectation by a large amount is a fascinating subject because of its relation to some ...
Conditional and uniform quenched CLTs for one-dimensional random walks among random conductances
one-dimensional random walks random conductances
2010/11/11
We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform elliptic...
Current fluctuations for independent random walks in multiple dimensions
Independent random walks hydrodynamic limit current Independent random walks
2010/12/6
Consider a system of particles evolving as independent and iden-tically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity ~v, the c...