Quaternionic Brownian Windings

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

Uperieure S Ormale N Ecole Stable Windings Stable Windings Stable Windings

We derive the asymptotic laws of winding numbers for planar isotropic stable L evy processes and walks of index 2 (0; 2).

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...

Quaternionic Line-Sets and Quaternionic Kerdock Codes

When n is even, orthogonal spreads in an orthogonal vector space of type O-(2n 2,2) are used to construct line-sets of size (2nm1 + 1)2”-’ in W2”~’ all of whose angles are 90” or cos -1(2-(“-2)/2). These line-sets are then used to obtain quatemionic Kerdock Codes. These constructions are based on ideas used by Calderbank, Cameron, Kantor, and Seidel in real and complex spaces.