The asymptotic joint distribution of windings of planar Brownian motion

Anyonic partition functions and windings of planar Brownian motion.

The computation of the N-cycle brownian paths contribution FN (α) to the N-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that F (0) N (α) = ∏N−1 k=1 (1 − N k α). In the paramount 3-anyon case, one can show that F3(α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S3. IPNO/TH 94-55 June...

The Accuracy of Cauchy Approximation for the Windings of Planar Brownian Motion

Asymptotic Windings of Horocycles

We analyze the scaling limits of the winding process for horocycles on non-compact hyperbolic surfaces with finite area. Initial conditions with pre-compact forward geodesics have scaling limits with gaussian and Cauchy components. Typical initial conditions have different scaling limits along different subsequences of times, but all such scaling limits can still be described. Some of our resul...

The Patched Brownian Motion Distribution

Windings of planar stable processes

Using a generalization of the skew-product representation of planar Brownian motion and the analogue of Spitzer’s celebrated asymptotic Theorem for stable processes due to Bertoin and Werner, for which we provide a new easy proof, we obtain some limit Theorems for the exit time from a cone of stable processes of index α ∈ (0, 2). We also study the case t → 0 and we prove some Laws of the Iterat...