Correlation functions as a tool to study collective behaviour phenomena in biological systems

Abstract

Much of interesting complex biological behaviour arises from collective properties. Importantinformation about collective behaviour lies in the time and space structure of fluctuations aroundaverage properties, and two-point correlation functions are a fundamental tool to study thesefluctuations. We give a self-contained presentation of definitions and techniques for computationof correlation functions aimed at providing students and researchers outside the field of statisticalphysics a practical guide to calculating correlation functions from experimental and simulationdata. We discuss some properties of correlations in critical systems, and the effect of finite systemsize, which is particularly relevant for most biological experimental systems. Finally we apply theseto the case of the dynamical transition in a simple neuronal model.