In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, a determinantal point process is a
stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...
point process
In statistics and probability theory, a point process or point field is a set of a random number of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Kallenberg, O. (1986). ''Random Measures'', ...
, the
probability distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...
of which is characterized as a
determinant
In mathematics, the determinant is a Scalar (mathematics), scalar-valued function (mathematics), function of the entries of a square matrix. The determinant of a matrix is commonly denoted , , or . Its value characterizes some properties of the ...
of some function. They are suited for modelling global negative correlations, and for efficient algorithms of sampling, marginalization, conditioning, and other inference tasks. Such processes arise as important tools in
random matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the ...
theory,
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
,
physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
,
machine learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
,
and wireless network modeling.
[N. Deng, W. Zhou, and M. Haenggi. The Ginibre point process as a model for wireless networks with repulsion. ''IEEE Transactions on Wireless Communications'', vol. 14, pp. 107-121, Jan. 2015.]
Introduction
Intuition
Consider some positively charged particles confined in a 1-dimensional box