Ofer Busani's homepage

I am a Lecturer (Assistant Professor) at the university of Edinburgh. I am mainly interested in probabilistic models that have strong connections to statistical physics.
In particular, I am interested in the Kardar-Parisi-Zhang (KPZ) universality class where one can find random growth processes, interacting particle systems, random polymers, stochastic PDEs and many other interesting models.

I am looking for a PhD student starting starting in 2026–27, if you are interested please apply here.

To get a better feel for the type of problems I’m interested in, let us look at a very classical example: the corner growth model (CGM). We place ourselves on the lattice \(\mathbb{Z}^2\), rotated by \(45^\circ\). At time zero, we declare some sites to be infected (blue vertices) while the rest remain healthy (black vertices). Each site of the lattice is assigned a random weight, independent and identically distributed. The dynamics are simple to describe: a site becomes eligible for infection (the purple vertices) once both of the sites directly below it are already infected. At that moment, we wait for a period of time equal to its random weight, after which the site itself flips from healthy to infected. This iterative mechanism drives the infection forward and produces the evolving random growth that we want to study.

A few natural questions arise at this point. Starting from a given infected set, should we indeed see the emergence of a macroscopic shape (shown below in red) as time grows? What can we say about the properties of this shape? Beyond that, what can be said about the scale of the fluctuations around it — in other words, how closely must we zoom in (what are the relevant dimensions of the rectangle below) in order to observe non-trivial random behaviour?