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The partition function for the random walk of an electrostatic field producedby several static parallel infinite charged planes in which the chargedistribution could be either $\pm\sigma$ is obtained. We find the electrostaticenergy of the system and show that it can be analyzed through generalized Dyckpaths. The relation between the electrostatic field and generalized Dyck pathsallows us to sum over all possible electrostatic field configurations and isused for obtaining the partition function of the system. We illustrate ourresults with one example.

Exact Partition Function for the Random Walk of an Electrostatic Field