Sojourn times of Markov symmetric processes in continuous time

TL;DR

This paper analyzes the sojourn times of symmetric birth and death processes in continuous time, exploring their implications for matter-antimatter asymmetry through stochastic modeling.

Contribution

It introduces a stochastic model using symmetric birth and death processes to explain matter-antimatter imbalance based on inhomogeneous sojourn times.

Findings

The process spends more time near the lower states, indicating matter dominance.

Long paths toward equilibrium suggest slow stochastic dynamics.

The model links sojourn times to matter-antimatter asymmetry in the universe.

Abstract

The symmetric birth and death process in the integers $\{1, \ldots, N \}$ with linear rates is studied. The process moves slowly and spends more time in the neighborhood of the state 1. It represents our attempt at explaining the asymmetry between amounts of matter and antimatter by the inhomogeneity of the sojourn time. The state of the process reflects a relative frequency of an antimatter amount. The observed matter-antimatter imbalance in the Universe we consider a result of stochastic competition between them. The amount of matter significantly exceeds the amount of antimatter, which corresponds to the lower states of the process, and the path toward matter-antimatter equilibrium can be very long.