Will FitzGerald

I am a postdoctoral researcher at the University of Manchester. My research interests are in probability theory often motivated by applications in mathematical physics. Previously I was a postdoc at Sussex and a PhD student at Warwick supervised by Jon Warren. A few of the topics I am interested in are shown below. My email address is william.lastname@manchester.ac.uk.

Random growth

How does a bacterial colony grow in a petri-dish? Why does this share the same behaviour as the spread of a flame across a piece of paper or the transport of spin in quantum magnets? In spite of being governed by different microscopic laws these systems all form part of the same universality class named Kardar-Parisi-Zhang (KPZ). My work in this area includes:

• Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions
• The invariant measure of PushASEP with a wall and point-to-line last passage percolation
• Pushing, blocking and Polynuclear growth

Ballistic Deposition

Interacting particle systems

Many natural phenomena involve large systems of particles that move around and interact with each other. These interactions could be repelling nearby particles, chemically reacting or adopting the spin/state of a neighbouring particle. How do these local interactions translate into the global behaviour of a system of particles? My research on interacting particle systems includes the q-state Potts model, coalescing/annihilating particle systems, last passage percolation, tandem queueing networks and PushASEP.

• Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems
• Ordered exponential random walks
• The invariant measure of PushASEP with a wall and point-to-line last passage percolation

The q-state Potts model evolving under Glauber dynamics

Random matrices

Around 1950, Eugene Wigner observed that the energy levels of large quantum systems depend only on their symmetry type and can be modelled by the eigenvalues of large random matrices. Since then random matrices have found many varied applications ranging from wireless communications to the selection of financial portfolios. My work in this area has focused on the real eigenvalues of non-Hermitian random matrices.

• Fluctuations and correlations for products of real asymmetric random matrices
• Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems
• Sharp asymptotics for Fredholm Pfaffians related to interacting particle systems and random matrices

Eigenvalues of products of real Ginibre random matrices