Random walks, Kleinian groups, and bifurcation currents     Random walks  Kleinian groups  bifurcation currents       font style='font-size:12px;'> 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...

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Upper tails of self-intersection local times of random walks: survey of proof techniques     self-intersection  random walks       font style='font-size:12px;'> 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 ...

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Conditional and uniform quenched CLTs for one-dimensional random walks among random conductances     one-dimensional random walks  random conductances       font style='font-size:12px;'> 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...

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Current fluctuations for independent random walks in multiple dimensions      Independent random walks  hydrodynamic limit  current Independent random walks       font style='font-size:12px;'> 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...

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