Getting Asymptotic Results from a Generating Function

Statistical Physics and Complexity Group meeting

Getting Asymptotic Results from a Generating Function

Event details

In this talk I will present a problem I have encountered in my own research, following on from a previous talk. I am trying to find a Rényi entropy of the Asymmetric Exclusion Process. In this nonequilibrium system, billiard ball-like particles hop along a discrete lattice. Notably, I want to find how this entropy scales with system size, and in different areas of the phase diagram.

We have managed to find “all at once” a particular Rényi entropy for all system sizes, in the form of a generating function. This is a closed form of a power series, with coefficients corresponding to different system sizes. I will show broadly how a generating function is analysed to find the asymptotic scaling of its coefficients – in our case this finds the Rényi entropy for large systems.