# Limit theorems for sticky particle systems and positivity of integrated random walks

# Limit theorems for sticky particle systems and positivity of integrated random walks

Consider the model of a one-dimensional gas, whose particles have random initial positions and random initial velocities. Particle attract each other due to gravitation, and stick together at collisions. As time goes, the number of particles decreases while their sizes increase until there forms a giant single particle of the total mass.The results on this process of mass aggregation are given in form of limit theorems as the number of initial particles tends to infinity. For example, the stochastic processes of the total number of particles satisfy a functional central limit theorem. I will show how this problem on the number of particles is related to positivity of integrated random walks. I will discuss the problem of finding one-sided small deviation probabilities of integrated random walks and other stochastic processes, and tell about the progress in this field.