scholarly journals Spaces of Lorentzian and real stable polynomials are Euclidean balls

2021 ◽  
Vol 9 ◽  
Author(s):  
Petter Brändén
Keyword(s):  
Interacting Particle Systems ◽  
Exclusion Process ◽  
Projective Spaces ◽  
Particle Systems ◽  
Stable Polynomials ◽  
Interacting Particle

Abstract We prove that projective spaces of Lorentzian and real stable polynomials are homeomorphic to Euclidean balls. This solves a conjecture of June Huh and the author. The proof utilises and refines a connection between the symmetric exclusion process in interacting particle systems and the geometry of polynomials.

scholarly journals Dynamics of interacting particle systems

2020 ◽  
Vol 68 ◽  
pp. 52-72
Author(s):  
Oriane Blondel ◽  
Aurelia Deshayes ◽  
Cyril Labbé ◽  
Laure Marêché ◽  
Marielle Simon
Keyword(s):  
Hydrodynamic Limit ◽  
Interacting Particle Systems ◽  
Mixing Time ◽  
Exclusion Process ◽  
Front Propagation ◽  
Particle Systems ◽  
Asymmetric Exclusion Process ◽  
Cutoff Phenomenon ◽  
Interacting Particle ◽  
Dynamical Properties

We collect here recent results covering various aspects of the dynamical properties of interacting particle systems. In Section 1 we study the hydrodynamic limit of a facilitated exclusion process. Section 2 evidences a cutoff phenomenon for the mixing time of the weakly asymmetric exclusion process. Section 3 presents a study of the infection time in the Duarte model. Finally, Section 4 presents the study of a front propagation in the FA-If model.

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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