The main aim of our research is to develop mathematical framework for the study of a class of stochastic systems of a large number of elements (called "particles") described by their "positions" and "marks" (representing internal structure of the corresponding particles). The particles are coupled via (random) interaction potentials. Examples of systems of such type can be found in a wide variety of sciences, including quantum physics, astrophysics, chemical physics, biology, ecology, computer science, economics, finance, etc.
Participating institutions: University of York, University of Wales-Swansea, University of Reading, University of Durham
PhD students: Tayfun Kok, Georgy Chargazia, Habeebat Ibraheem, Maryam Alshehri, Adam Barker, Joey McMillan
International collaboration: Professor Yuri Kondratiev, Dr Tanja Pasurek, Dr Oles Kutovyi (Bielefeld), Dr Maria Infusino (Konstanz), Professor Yuri Kozitsky (Lublin), Dr Diana Conache (Muenchen)
Recent selected publications:
D. Conache, Y. Kondratiev, E. Lytvynov: Equilibrium diffusion on the cone of discrete Radon measures, arXiv:1503.04166, to appear in Potential Analysis
Y. Kondratiev, E. Lytvynov, A. Vershik: Laplace operators on the cone of Radon measures, arXiv:1503.00750, to appear in J. Funct. Anal.
Y. Kondratiev, T. Kuna, E. Lytvynov: A moment problem for random discrete measures, Stochastic Process. Appl. 125 (2015), 3541-3569
D. Conache, A. Daletskii, Yu. Kondratiev, T. Pasurek: Gibbs Measures on Marked Configuration Spaces: Existence and Uniqueness, arXiv:1503.06349 [math-ph] (2015).
A. Daletskii, Yu. Kondratiev, Yu. Kozitsky: Phase Transitions in Continuum Ferromagnets with Unbounded Spins, arXiv:1503.07010 [math-ph] (2015).
A. Daletskii, Yu. Kondratiev, Yu. Kozitsky, T. Pasurek: Phase Transitions in a quenched amorphous ferromagnet, J. Stat. Phys. (2014) 156:156—176.
A. Daletskii, Yu. Kondratiev, Yu. Kozitsky, T. Pasurek: Gibbs states on random configurations (with Yu. Kondratiev, Yu. Kozitsky, T. Pasurek), J. Math. Phys. 55, 083513 (2014).
Finkelshtein, D. Around Ovsyannikov's method. Methods of Functional Analysis and Topology, (2015) 21(2), 134-150.
Finkelshtein, D., Kondratiev, Y., Kozitsky, Y. Kutoviy, O. The statistical dynamics of a spatial logistic model and the related kinetic equation. Mathematical Models and Methods in Applied Sciences, (2015) 25(02), 343-370, doi:10.1142/S0218202515500128
Finkelshtein, D., Kondratiev, Y., Kutoviy, O. Oliveira, M. Dynamical Widom–Rowlinson Model and its Mesoscopic Limit. Journal of Statistical Physics, (2015) 158(1), 57-86, doi:10.1007/s10955-014-1124-6
Events: - the following meetings are partly funded by an LMS Joint Research Groups in the UK - Scheme 3 grant.
MMRMS Workshop 1 - December 2015
MMRMS Workshop 2 - February 2016
MMRMS Workshop 3 - June 2016
MMRMS Workshop 4 - September 2016
MMRMS Workshop 5 - March 2017
MMRMS Workshop 6 - November 2017
MMRMS Workshop 7 - May 2018