Brownian Fluctuations of a non-confining potential

Brownian fluctuations arise for any quantity that depends on the stochastic variables of a Brownian particle. In this study, we explore the Brownian fluctuations of a bidimensional quadratic potential that exhibits two regimes: a confining regime and a non-confining regime. We divide the total potential into two contributions and analyze the mean, variance, skewness, excess kurtosis, and their distributions for each contribution as well as for the total potential. Our analysis offers an understanding into the statistical behavior of each quantity.