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 $\pm\sigma$ 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 over all possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.
Fractional derivatives of random walks: Time series with long-time memory
Exact Partition Function for the Potts Model with Next-Nearest Neighbor Couplings on Strips of the Square Lattice
Critical exponents of correlated percolation of sites not visited by a random walk
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