Spatial Coalescent Models
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
The proposal is an investigation into models involving spatial coalescence, with the broad aim of gaining an understanding of the evolutions of models involving these mechanisms, for example in their dynamics or stationary distributions, but also, especially in applied settings, for the universal features of their spatial and temporal statistics, for example via the derivation of concrete scaling laws for associated probabilities and expectations in terms of the model parameters.
In particular to gain an understanding of:
I. Large time density estimates for multi-species coalescence models;
II. Negative correlations properties for models with coalescence;
III. Pfaffian, and extended Pfaffian, properties for the particle densities, and joint particle-mass densities, for spatial models with coalescence;
IV. Steady states for coalescent models with immigration;
V. The evolution for the eigenvalues for the real Ginibre matrices and its connection with annihilating systems.
In particular to gain an understanding of:
I. Large time density estimates for multi-species coalescence models;
II. Negative correlations properties for models with coalescence;
III. Pfaffian, and extended Pfaffian, properties for the particle densities, and joint particle-mass densities, for spatial models with coalescence;
IV. Steady states for coalescent models with immigration;
V. The evolution for the eigenvalues for the real Ginibre matrices and its connection with annihilating systems.
Planned Impact
The national impact of the work in this proposal can be summarized as:
1. Strengthening of the knowledge base within the field of particle systems for problems involving spatial coalescence, putting the UK at the cutting edge in this active area.
2. Creation of a UK group investigating an interlocking set of tools and applications in this area.
3. Training of young mathematicians for their future careers in science.
4. A contribution to the UK's provision for applied probability by targeting some of the group towards applications ranging from aggregation models in astronomy to interacting financial agents.
1. Strengthening of the knowledge base within the field of particle systems for problems involving spatial coalescence, putting the UK at the cutting edge in this active area.
2. Creation of a UK group investigating an interlocking set of tools and applications in this area.
3. Training of young mathematicians for their future careers in science.
4. A contribution to the UK's provision for applied probability by targeting some of the group towards applications ranging from aggregation models in astronomy to interacting financial agents.
Organisations
Publications
Borodin A
(2016)
Erratum to: The Ginibre Ensemble of Real Random Matrices and its Scaling Limits
in Communications in Mathematical Physics
Lukins J
(2019)
Multi-point correlations for two-dimensional coalescing or annihilating random walks
in Journal of Applied Probability
Connaughton C
(2013)
Non-equilibrium Phase Diagram for a Model with Coalescence, Evaporation and Deposition
in Journal of Statistical Physics
Poplavskyi M
(2016)
On the distribution of the largest real eigenvalue for the real Ginibre ensemble
Poplavskyi M
(2017)
On the distribution of the largest real eigenvalue for the real Ginibre ensemble
in The Annals of Applied Probability
FitzGerald W
(2020)
Sharp asymptotics for Fredholm Pfaffians related to interacting particle systems and random matrices
in Electronic Journal of Probability
Kanzieper E
(2016)
What is the probability that a large random matrix has no real eigenvalues?
in The Annals of Applied Probability
Kanzieper E
(2015)
What is the probability that a large random matrix has no real eigenvalues?