Alladi Ramakrishnan Hall

Higher-order correlators in the Random Average Process

Rahul Dandekar

IMSc

The Random Average Process (RAP) is a simple model of single file motion on a 1D line, where at each time-step, particles move by a random fraction of the distance to the next particle. In this talk, I will describe work with Anupam Kundu at ICTS, Bangalore, where we found that due to the linear nature of this update, all higher-order two-point cumulants can be expressed in terms of the lowest order two-point cumulant, the site-site correlation function . This can be extended to the multi-site cumulants as well. Simple analytic expressions will be derived for the generating function of two- and three-site cumulants. This uncovers a previously unknown structure in the Random Average Process, and I shall talk about the case of the RAP with open boundaries as a concrete example where this simplification can be usefully applied.