# Wright-Fisher-type equations for opinion formation, large time behavior and weighted logarithmic-Sobolev inequalities

## TL;DR

This paper investigates the long-term behavior of a Fokker-Planck equation modeling opinion formation, focusing on convergence rates and mathematical challenges posed by variable diffusion and boundary conditions.

## Contribution

It introduces new mathematical analysis for a Fokker-Planck equation with variable diffusion, providing insights into convergence to equilibrium in opinion dynamics.

## Key findings

- Derived convergence rates to equilibrium
- Analyzed effects of variable diffusion and boundaries
- Established new inequalities related to the model

## Abstract

We study the rate of convergence to equilibrium of the solution of a Fokker--Planck type equation introduced by one of the authors in 2006 to describe opinion formation in a multi-agent system. The main feature of this Fokker--Planck equation is the presence of a variable diffusion coefficient and boundaries, which introduce new challenging mathematical problems in the study of its long-time behavior.