Scaling Limit of a Generalized Contact Process

Logan Chariker, Anna De Masi, Joel L. Lebowitz, Errico Presutti

Research output: Contribution to journalArticlepeer-review


We derive macroscopic equations for a generalized contact process that is inspired by a neuronal integrate and fire model on the lattice Zd. The states at each lattice site can take values in 0 , … , k. These can be interpreted as neuronal membrane potential, with the state k corresponding to a firing threshold. In the terminology of the contact processes, which we shall use in this paper, the state k corresponds to the individual being infectious (all other states are noninfectious). In order to reach the firing threshold, or to become infectious, the site must progress sequentially from 0 to k. The rate at which it climbs is determined by other neurons at state k, coupled to it through a Kac-type potential, of range γ- 1. The hydrodynamic equations are obtained in the limit γ→ 0. Extensions of the microscopic model to include excitatory and inhibitory neuron types, as well as other biophysical mechanisms, are also considered.

Original languageEnglish (US)
Article number49
JournalJournal of Statistical Physics
Issue number3
StatePublished - Mar 2023

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Generalized contact process
  • Hydrodynamic limit
  • Integrate and fire
  • Mean field
  • Neurons with discrete voltage
  • Spatial dependence


Dive into the research topics of 'Scaling Limit of a Generalized Contact Process'. Together they form a unique fingerprint.

Cite this