Universality in Stochastic Exponential Growth

Universality in stochastic exponential growth.

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponen...

Phenomenology of stochastic exponential growth.

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solut...

Stretched exponential relaxation and ac universality in disordered dielectrics

Universality of the Stochastic Airy Operator

We introduce a new method for studying universality of random matrices. Let Tn be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that after scaling, Tn converges to the Stochastic Airy operator. In particular, the top edge of the Dyson beta ensemble and the corresponding eigenvectors are universal. As a byproduct, our work leads to co...

Non - Exponential Stochastic Petri Nets :

The aim of this tutorial is to present recent research work in the area of non-Markovian stochas-tic Petri nets with particular emphasis on the se-mantical implication of these models, their speci-cation and the related solution techniques.