Anyonic partition functions and 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

Brownian Motion and Harmonic Functions

The Lie group Sol(p, q) is the semidirect product induced by the action of R on R which is given by (x, y) 7→ (ex, e−qzy), z ∈ R. Viewing Sol(p, q) as a 3-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift term in the z-variable to the latter, and study the associated Brownian motion with drift. We derive a central limit theorem and...

Logarithmic Potentials and Planar Brownian Motion

In Section 5, we saw that for a Brownian motion process in n _ 3 dimensions, P (limtxIX, = o0) = 1 for all x. In sharp contrast to this situation, a planar Brownian motion is certain to hit any nonpolar set. THEOREM 8.1. Let B be a Borel set. Then PX(VB < cX) is either identically 1 or identically 0. PROOF. A simple computation shows that for any x e R2, 1' p(s, x) ds T co as t T oc. Thus, for ...

Multiple intersection exponents for planar Brownian motion

Let p ≥ 2, n1 ≤ · · · ≤ np be positive integers and B 1 , . . . , B n1 ; . . . ;B p 1 , . . . , B np be independent planar Brownian motions started uniformly on the boundary of the unit circle. We define a p-fold intersection exponent ςp(n1, . . . , np), as the exponential rate of decay of the probability that the packets ⋃ni j=1 B i j [0, t ], i = 1, . . . , p, have no joint intersection. The ...