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Advances in Mathematical Physics
Volume 2017, Article ID 6970870, 5 pages
https://doi.org/10.1155/2017/6970870
Research Article

Exact Partition Function for the Random Walk of an Electrostatic Field

1Cátedras CONACYT, Universidad Autónoma de San Luis Potosí, 78000 San Luis Potosí, SLP, Mexico
2Coordinación para la Innovación y la Aplicación de la Ciencia y la Tecnología, Universidad Autónoma de San Luis Potosí, 78000 San Luis Potosí, SLP, Mexico

Correspondence should be addressed to Gabriel González; xm.plsau@zelaznog.leirbag

Received 7 April 2017; Revised 6 June 2017; Accepted 14 June 2017; Published 13 July 2017

Academic Editor: Jacopo Bellazzini

Copyright © 2017 Gabriel González. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either is obtained. We find the electrostatic energy of the system and show that it can be analyzed through generalized Dyck paths. The relation between the electrostatic field and generalized Dyck paths allows us to sum overall possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.