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The rate of escape for random walks on polycyclic and metabelian groups

Russ Thompson (2013)

Annales de l'I.H.P. Probabilités et statistiques

We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on some abelian-by-cyclic groups via a comparison to the toppling of a dissipative abelian...

The Ray space of a right process

Ronald K. Getoor, Michael J. Sharpe (1975)

Annales de l'institut Fourier

Let X be a process with state space E satisfying (a somewhat relaxed version of) Meyer’s “hypothèses droites”. Then by introducing a new topology (called the Ray topology) on E and a compactification F of E in the Ray topology one can regard X as a Ray process. However, this construction depends on the choice of an arbitrary uniformity on E and not just the topology of E . We show that the Ray topology is independent of the choice of this uniformity. We then introduce a space R (the Ray space) which...

The right tail exponent of the Tracy–Widom β distribution

Laure Dumaz, Bálint Virág (2013)

Annales de l'I.H.P. Probabilités et statistiques

The Tracy–Widom β distribution is the large dimensional limit of the top eigenvalue of β random matrix ensembles. We use the stochastic Airy operator representation to show that as a → ∞ the tail of the Tracy–Widom distribution satisfies P ( 𝑇𝑊 β g t ; a ) = a - ( 3 / 4 ) β + o ( 1 ) exp - 2 3 β a 3 / 2 .

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