Speaker
Abdelmalek Abdesselam
(Virginia Univ. (USA))
Description
Hierarchical models a.k.a. the approximate recursion played a
fundamental role in the discovery
of the epsilon-expansion for critical exponents by Wilson and Fisher. In
a not so well known 1972 article,
Wilson showed, at the heuristic level, that at a nontrivial hierarchical
model fixed point, the elementary field
has no anomalous scaling whereas the composite square field does have
one. I will report on a joint work with Ajay Chandra and Gianluca
Guadagni on a particular hierarchical model, the p-adic model, which
rigorously proves Wilson's prediction. The two main ideas are a
constructive renormalization group for space dependent couplings and a
holomorphic partial linearization theorem in infinite dimension, in the
spirit of Wegner's theory of nonlinear scaling fields. I will also
report on recent progress I am making in the analysis of short distance
behavior such as the pointwise representability of correlation
functions. The goal is to prove the operator product expansion and
generalize the pathwise construction of squares of random distributions
given by Wick powers to the setting of a nontrivial fixed point with
anomalous dimensions.
Primary author
Abdelmalek Abdesselam
(Virginia Univ. (USA))
