In this note, we study the high-temperature convolution introduced in Ref.\ \cite{ mergny_cconv}, between two symmetric Bernoulli distributions. We give an analytical expression for both the Stieltjes transform and the density. This result provides the first non-trivial expression for the high-temperature convolution of two distributions and gives a new family of densities, interpolating between the centered binomial distribution with number of trials $n{ =}2$ and probability of success $p{ =}1/2$, and the centered and re-scaled arcsine law.
Categories: cond-mat.stat-mech math.PR