the search for a global minimum of a function using the simulated annealing algorithm.'
address:
- |
    Department of Electrical Communication Engineering\
    Indian Institute of Science\
    Bangalore 560012, India\
- |
    Department of Electrical Communication Engineering\
    and Robert Bosch Centre for Cyber Physical Systems\
    Indian Institute of Science\
    Bangalore 560012, India\
author:
- 
- 
bibliography:
- 'ims-template.bib'
title: 'Large Time Behaviour and the Second Eigenvalue Problem for Finite State Mean-Field Interacting Particle Systems'
---

Introduction {#section:introduction}
============

In this paper, we study large time behaviour and the second eigenvalue problem for Markovian mean-field interacting particle systems with jumps. Our motivation is to provide an understanding of metastable phenomena in engineered systems such as load balancing networks [@aghajani-etal-17; @aghajani-ramanan-19; @mukhopadhyay-etal-16; @mitzhenmaker-00; @graham-00], wireless local area networks [@bhattacharya-kumar-17; @benaim-leboudec-08; @bordenave-etal-12; @kumar-etal-06; @ramaiyan-etal-08; @bianchi-98], and in natural systems involving grammar acquisition, sexual evolution [@panageas-vishnoi-16; @panageas-etal-16], epidemic spread [@leonard-90; @djehiche-kaj-95], etc. These systems are briefly described in Section \[section:examples\].

Before we describe our main contributions, let us describe the setting of our mean-field interacting particle system.

The setting
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Let there be $N$ particles. Each particle has a state associated with it which comes from a finite set $\mathcal{Z}$; the state of the $n$th 