Random walks as Euclidean field theory (EFT)
An identity is derived which represents a lattice field theory in terms of interacting (“non-simple”) random walks.
Inequalities are derived which bound certain connected correlation functions of the field theory (in particular, the dimensionless renormalized coupling constant g) in terms of the intersection properties of these “field-theoretic” random walks.
The intersection properties of simple random walks are used as intuition to motivate conjectures for the intersection properties of “field-theoretic” random walks (These conjectures must, however, be proven by different methods.)
KeywordsIntersection Property Hausdorff Dimension Simple Random Walk Intersection Probability Brownian Path
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