A Monad for Probabilistic Point Processes

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.

Download Full-text

Coloring spatial point processes with applications to peer discovery in large wireless networks

Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '10 ◽

10.1145/1811039.1811059 ◽

2010 ◽

Cited By ~ 7

Author(s):

Jian Ni ◽

R. Srikant ◽

Xinzhou Wu

Keyword(s):

Wireless Networks ◽

Point Processes ◽

Spatial Point Processes ◽

Spatial Point

Download Full-text

A Termination Criterion for Probabilistic Point Clouds Registration

Signals ◽

10.3390/signals2020013 ◽

2021 ◽

Vol 2 (2) ◽

pp. 159-173

Author(s):

Simone Fontana ◽

Domenico Giorgio Sorrenti

Keyword(s):

State Of The Art ◽

Point Clouds ◽

Computational Time ◽

Termination Criteria ◽

Practical Usefulness ◽

Local Point ◽

Termination Criterion ◽

Probabilistic Point ◽

Excessive Number ◽

Number Of Iterations

Probabilistic Point Clouds Registration (PPCR) is an algorithm that, in its multi-iteration version, outperformed state-of-the-art algorithms for local point clouds registration. However, its performances have been tested using a fixed high number of iterations. To be of practical usefulness, we think that the algorithm should decide by itself when to stop, on one hand to avoid an excessive number of iterations and waste computational time, on the other to avoid getting a sub-optimal registration. With this work, we compare different termination criteria on several datasets, and prove that the chosen one produces very good results that are comparable to those obtained using a very large number of iterations, while saving computational time.

Download Full-text

Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2020.123 ◽

2020 ◽

pp. 1-14

Author(s):

SHOTA OSADA

Keyword(s):

Point Processes ◽

Duke Math ◽

Random Point ◽

Determinantal Point Processes ◽

Fredholm Determinants ◽

Poisson Point Processes ◽

Translation Invariant ◽

Ergodic Properties ◽

Tree Representations ◽

Invariant Kernels

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

Download Full-text