New probability distribution describing emergence in state space

TL;DR

This paper introduces a simplified pairing model for state spaces, computes exact probability distributions for emergent states, and demonstrates a large deviation principle with explicit statistical expressions.

Contribution

It provides a new simplified pairing model and exact probability distributions, advancing understanding of emergent states in state space models.

Findings

Probability distribution for number of pairs computed exactly

Distribution satisfies a large deviation principle with speed n log(n)

Closed-form expressions for moments and marginal distributions

Abstract

We revisit the pairing model of state spaces with new emergent states introduced in J. Phys. A: Math. Theor. 51 375002, 2018. We facilitate our analysis by introducing a simplified pairing model consisting of balls able to form pairs but without any internal structure. For both the simplified and the original model we compute exactly the probability distribution for observing a state with $n_p$ pairs. We show this distribution satisfies a large deviation principle with speed $n \ln(n)$. We present closed form expressions for a variety of statistical quantities including moments and marginal distributions.