Dr. W.M. (Wioletta) Ruszel

Hans Freudenthalgebouw
Budapestlaan 6
Kamer 516
3584 CD Utrecht

Dr. W.M. (Wioletta) Ruszel

Universitair hoofddocent
Mathematical Modeling
030 253 1459

I am working in the intersection of probability theory and mathematical physics.

Spin models from statistical mechanics describe collective macroscopic behaviour of many interacting objects from individual local interactions. Due to the large degree of freedom and some physical properties, those mathematical models can only be described in a probabilistic way, by e.g. Gibbs measures. Those models display a wide range of critical phenomena, such as: existence of multiple infinite volume measures, emergence of separation lines or synchronization.

In particular, I am fascinated by the following questions:

  • Abelian sandpile model on random trees, connections to logarithmic conformal field theories, models of self-organized criticality
  • construction and properties of random interface models such as fractional Gaussian fields (Gaussian free field, bi-Laplacian field) or Dobrushin interfaces which are natural models of phase separation
  • synchronization phenomena for Kuramoto models
  • transformations of Gibbs measures that preserve/destroy the Gibbs property
  • understanding and generalizing mathematical techniques such as fractional Edgeworth expansions, contour methods for nonlocal models, Pirogov-Sinai theory