Research

Research interests 

My research area is Probability Theory. Probability -while extremely applicable- has a deep theoretical foundation. That being said, the origins do lie in gambling, so any probabilist before proving theorems first rolls dice and tosses coins.

A big chunk of my research is dedicated to random spatial processes, particularly last passage percolation (LPP). I would be very happy to broadly explain the area to anyone interested. Loosely speaking, LPP studies the evolution (growth) of a temporally, ever-growing random cluster. As an example, consider a stain on piece of cloth. The evolution depends on the underlying structures (e.g. cloth material) and the random environment (type of liquid and inhomgeneities in cloth). 

One of the best aspects of directed last passage percolation is an equivalence with a particle system called a totally asymmetric simple exclusion process (TASEP). This system can model queues in tandem and single lane highway traffic. 

My two most recent papers on these topics are on the mathematics arXiv. They are written together with my Ph.D. student, Federico Ciech 

 

  1. Order of the variance for the discrete Hammersley process with boundaries 
  2. Last passage percolation in an exponential environment with discontinuous rates

 

Expository articles and public engagement

I strongly believe in communicating mathematics outside of mathematics or sciences. Together with Prof. Enrico Scalas, we wrote two expository articles for The Conversation, that were later picked up for publication in other places, like the Newsweek:

  1. There's a mathematical formula for choosing the fastest queue (with E. Scalas), 7 May, 2017 
  2. Can Opinion polls ever be accurate? Probably not (with E. Scalas), 21 June, 2016   

 

Keywords

Probability theory, particle systems, hydrodynamic limits, large deviation theory, random spatial processes, queues