scholarly journals Parametric estimation of pairwise Gibbs point processes with infinite range interaction

Bernoulli ◽  
2017 ◽  
Vol 23 (2) ◽  
pp. 1299-1334 ◽  
Author(s):  
Jean-François Coeurjolly ◽  
Frédéric Lavancier
Keyword(s):  
Point Processes ◽  
Parametric Estimation ◽  
Range Interaction ◽  
Gibbs Point Processes ◽  
Infinite Range

scholarly journals Existence of Gibbs point processes with stable infinite range interaction

2020 ◽  
Vol 57 (3) ◽  
pp. 775-791
Author(s):  
David Dereudre ◽  
Thibaut Vasseur
Keyword(s):  
Point Processes ◽  
Existence Results ◽  
Pairwise Interaction ◽  
Range Interaction ◽  
Pairwise Interactions ◽  
Gibbs Point Processes ◽  
Infinite Range Interactions ◽  
Finite Configuration ◽  
Multi Body ◽  
Infinite Range

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

scholarly journals Fast approximation of the intensity of Gibbs point processes

2012 ◽  
Vol 6 (0) ◽  
pp. 1155-1169 ◽  
Author(s):  
Adrian Baddeley ◽  
Gopalan Nair
Keyword(s):  
Point Processes ◽  
Gibbs Point Processes

scholarly journals Direct Scaling Analysis of Fermionic Multiparticle Correlated Anderson Models with Infinite-Range Interaction

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Victor Chulaevsky
Keyword(s):  
Dynamical Localization ◽  
Scaling Analysis ◽  
Range Interaction ◽  
Direct Scaling ◽  
Strongly Mixing ◽  
Optimal Decay ◽  
Decay Bounds ◽  
Multiparticle Systems ◽  
Infinite Range ◽  
Anderson Models

We adapt the method of direct scaling analysis developed earlier for single-particle Anderson models, to the fermionic multiparticle models with finite or infinite interaction on graphs. Combined with a recent eigenvalue concentration bound for multiparticle systems, the new method leads to a simpler proof of the multiparticle dynamical localization with optimal decay bounds in a natural distance in the multiparticle configuration space, for a large class of strongly mixing random external potentials. Earlier results required the random potential to be IID.

Sign in / Sign up

Export Citation Format

Share Document