Tyler Helmuth

The continuous-time lace expansion and it’s applications.

The lace expansion is one of the primary tools for proving that probability models in high dimensions have mean field behaviour. I will explain the previous sentence by describing joint work in progress with David Brydges and Mark Holmes in which we develop a continuous time lace expansion. To motivate our methods I will introduce a class of n-component field theories that are generalizations of the Ising model of ferromagnetism. When n is zero, one, or two we are able to analyze these models. Our results for the case n=2 are new.
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