Research Group

Stochastic Analysis in Mathematical Physics

We are interested in applications of Stochastic Analysis in Mathematical Physics, more specially in using probability to study Gibbs measures coming from Quantum Field Theory and Statistical Mechanics.


We are mainly interested in Euclidean Quantum Field Theories (EQFTs). These are measures on spaces distributions, typically build from a base Gaussian measure, the Gaussian Free Field. The distributional nature of these measures complicates their construction. EQFTs are closely related to Stochastic Partial Differential Equations, and share many common features, as well as to Stochastic Control, via the Boué-Dupuis formula.

Our Research Interests include:

  • Euclidean Quantum Field Theory,
  • Stochastic PDE's,
  • Stochastic Optimal Control,
  • Renormalisation. 

One of our Longterm Goals is understanding better the Large Scale properties of EQFTs (like decay of correlation functions), using techniques from SPDEs or Stochastic Control. 



Not yet available

The group does not have any publications at this time.

In the meantime, please browse Nikolay Barashkov's Publications