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Dr Marton Balazs

Interacting particle systems

Please see my personal webpage for information on my research.


Available PhD projects

Blocking measures and scaling in stochastic particle systems

Blocking measures are certain stationary distributions in stochastic interacting particle systems. They either have a relatively easy structure or when this is not the case then they are usually very hard to analyse. Because of these two extreme cases, processes in this kind of stationarity have been less investigated than under other scenarios. There are nevertheless many interesting questions of fluctuations and scaling limits in the area which this project will investigate. We will dive into various phenomena of stochastic particle systems, learning about stationary and quasi-stationary structures, scaling arguments, probabilistic couplings, and martingale techniques along the way.


Research keywords

  • Stochastic processes
  • Interacting systems
  • Probability theory