Nontrivial Exponent for Simple Diffusion

The Intersection Exponent For Simple Random Walk

The intersection exponent for simple random walk in two and three dimensions gives a measure of the rate of decay of the probability that paths do not intersect. In this paper we show that the intersection exponent for random walks is the same as that for Brownian motion and show in fact that the probability of nonintersection up to distance n is comparable (equal up to multiplicative constants...

A Class of Finite Simple Bol Loops of Exponent 2

In this paper we give an infinite class of finite simple right Bol loops of exponent 2. The right multiplication group of these loops is an extension of an elementary Abelian 2-group by S5. The construction uses the description of the structure of such loops given by M. Aschbacher (2005). These results answer some questions of M. Aschbacher.

Fast Diffusion Equation with Critical Sobolev Exponent in a Ball

Nontrivial directions for scalar fields.

We study the eigenvectors of the renormalization-group matrix for scalar fields at the Gaussian fixed point, and find that that there exist “relevant” directions in parameter space. They correspond to theories with exponential potentials that are nontrivial and asymptotically free. All other potentials, including polynomial potentials, are “irrelevant,” and lead to trivial theories. Away from t...

Trivial Generators for Nontrivial Fibres

Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in Cn where the fibre is nontrivial, has to exceed n. This is s...