Unveiling Order in Disorder: The Role of Conditionally Independent Random Variables in Strongly Correlated Systems
Marco Biroli (LPTMS)
In this seminar, I will introduce the concept of conditionally independent and identically distributed (CIID) random variables and demonstrate how they can be used to analytically describe certain strongly correlated systems. We will see that conditional independence is not merely an artificial construct; it also arises naturally in certain systems. Leveraging this structure, we will uncover surprising regularities and derive robust predictions across a variety of models.
Using examples from resetting systems and many-body stochastic models, I will illustrate how CIID variables serve as essential building blocks for modeling intricate, strongly correlated systems, leading to fascinating scaling phenomena. This seminar aims to provide a comprehensive understanding of the foundational theory of CIID variables and explore their practical applications.