ar X iv : m at h / 04 04 10 5 v 1 [ m at h . PR ] 5 A pr 2 00 4 What is the probability of intersecting the set of Brownian double points ?

ar X iv : m at h / 05 04 55 2 v 1 [ m at h . N T ] 2 7 A pr 2 00 5 Multiple logarithms , algebraic cycles and trees

This is a short exposition—mostly by way of the toy models " double logarithm " and " triple logarithm " —which should serve as an introduction to the article [3] in which we establish a connection between multiple polylogarithms, rooted trees and algebraic cycles.

ar X iv : m at h / 05 04 37 3 v 1 [ m at h . Q A ] 1 9 A pr 2 00 5 Lax Operator for the Quantised Orthosymplectic

ar X iv : m at h / 02 04 21 5 v 1 [ m at h . PR ] 1 7 A pr 2 00 2 Explicit Construction of the Brownian Self - Transport Operator

Applying the technique of characteristic functions developped for one-dimensional regular surfaces (curves) with compact support, we obtain the distribution of hitting probabilities for a wide class of finite membranes on square lattice. Then we generalize it to multi-dimensional finite membranes on hypercubic lattice. Basing on these distributions, we explicitly construct the Brownian self-tra...

ar X iv : m at h / 98 03 04 6 v 1 [ m at h . PR ] 1 1 M ar 1 99 8 LOCAL FIELDS , GAUSSIAN MEASURES , AND BROWNIAN MOTIONS Steven

ar X iv : m at h / 05 04 08 2 v 4 [ m at h . D G ] 1 5 A pr 2 00 6 COMPLETE PROJECTIVE CONNECTIONS

The first examples of complete projective connections are uncovered: on surfaces, normal projective connections whose geodesics are all closed and embedded are complete. On manifolds of any dimension, normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature are complete.