scholarly journals Examples of Interacting Particle Systems on $$\mathbb {Z}$$ Z as Pfaffian Point Processes: Annihilating and Coalescing Random Walks

2018 ◽  
Vol 19 (12) ◽  
pp. 3635-3662 ◽  
Author(s):  
Barnaby Garrod ◽  
Mihail Poplavskyi ◽  
Roger P. Tribe ◽  
Oleg V. Zaboronski
Keyword(s):  
Random Walks ◽  
Point Processes ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Interacting Particle ◽  
Coalescing Random Walks

scholarly journals Examples of Interacting Particle Systems on $$\mathbb {Z}$$ as Pfaffian Point Processes: Coalescing–Branching Random Walks and Annihilating Random Walks with Immigration

2019 ◽  
Vol 21 (3) ◽  
pp. 885-908
Author(s):  
Barnaby Garrod ◽  
Roger Tribe ◽  
Oleg Zaboronski
Keyword(s):  
Random Walks ◽  
Point Processes ◽  
Interacting Particle Systems ◽  
Initial Conditions ◽  
Fixed Time ◽  
Particle Systems ◽  
Branching Random Walks ◽  
Interacting Particle ◽  
Point Set ◽  
Annihilating Random Walks

AbstractTwo classes of interacting particle systems on $$\mathbb {Z}$$Z are shown to be Pfaffian point processes, at any fixed time and for all deterministic initial conditions. The first comprises coalescing and branching random walks, the second annihilating random walks with pairwise immigration. Various limiting Pfaffian point processes on $$\mathbb {R}$$R are found by diffusive rescaling, including the point set process for the Brownian web and Brownian net.

scholarly journals Condensation of SIP Particles and Sticky Brownian Motion

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Mario Ayala ◽  
Gioia Carinci ◽  
Frank Redig
Keyword(s):  
Brownian Motion ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Self Duality ◽  
Inclusion Process ◽  
Interacting Particle ◽  
New Information ◽  
Homogeneous Product ◽  
Coarsening Dynamics ◽  
The Difference

AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.

scholarly journals Holomorphic Bogoliubov functionals for interacting particle systems in continuum

2006 ◽  
Vol 238 (2) ◽  
pp. 375-404 ◽  
Author(s):  
Yuri G. Kondratiev ◽  
Tobias Kuna ◽  
Maria João Oliveira
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Interacting Particle
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