https://cea.hal.science/cea-01280137v1Epelbaum, ThomasThomasEpelbaumMcGill University = Université McGill [Montréal, Canada]Gelis, FrançoisFrançoisGelisIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueWu, BinBinWuDepartment of Physics [Columbus] - OSU - Ohio State University [Columbus]From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$HAL CCSD2016[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph][PHYS.HLAT] Physics [physics]/High Energy Physics - Lattice [hep-lat][PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]De Laborderie, EmmanuelleBLANC - Interactions multiples et production de particules au LHC - - CGC@LHC2011 - ANR-11-BS04-0015 - BLANC - VALID - 2016-02-29 10:25:372023-03-24 14:53:022016-03-02 10:04:37enJournal articleshttps://cea.hal.science/cea-01280137v1/document10.4171/AIHPD/33https://cea.hal.science/cea-01280137v1text/html; charset=utf-81In 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.