Publication

Characterization of equilibrium measures for critical reversible Nearest Particle Systems

Thomas Mountford
2008
Journal Articles

Abstract

We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than 7+root 4/2 and obeys some natural regularity conditions.

Official source

https://infoscience.epfl.ch/entities/publication/07444274-413b-4d65-be22-333159420d3b

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Thomas Mountford
2008
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/07444274-413b-4d65-be22-333159420d3b

About this result

Related concepts (16)

Total order

In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.

Partially ordered set

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, transitive and antisymmetric.

Convex combination

In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1. In other words, the operation is equivalent to a standard weighted average, but whose weights are expressed as a percent of the total weight, instead of as a fraction of the count of the weights as in a standard weighted average.

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