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From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$

Abstract : In theworldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the algebraic areas over the set of loops that have fixed number of edges in the two directions. We show that these moments are the product of a combinatorial factor that counts the number of such loops, by a polynomial in the numbers of steps in each direction. Our approach leads to an algorithm for obtaining explicit formulas for the moments of low order.
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https://hal-cea.archives-ouvertes.fr/cea-01280137
Contributor : Bruno Savelli Connect in order to contact the contributor
Submitted on : Wednesday, October 19, 2022 - 9:43:40 AM
Last modification on : Friday, October 21, 2022 - 3:34:10 AM

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Thomas Epelbaum, François Gelis, Bin Wu. From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$. Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2016, 3, pp.381-404. ⟨10.4171/AIHPD/33⟩. ⟨cea-01280137v2⟩

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