2024/12/06 by O. A. Dobush, Dobush, O. A., M. A. Shpot +1 · 4 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2412.05428
openalex publication_date 2024/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by previous studies in statistical physics [see, in particular, Kozitsky at al., A phase transition in a Curie-Weiss system with binary interactions, Condens. Matter Phys. 23, 23502 (2020)] we introduce a discrete Gauss-Poisson probability distribution function pGP(n ;z,r)=[R(r;z)]-1\fraceznn! e-\frac 12 rn2 with support on \mathbb N0 and parameters z∈\mathbb R and r∈\mathbb R+. The probability mass function pGP(n ;z,r) is normalized by the special function R(r;z), given by the infinite sum R(r;z)=∑n=0^∞\fraceznn! e-\frac 12 rn2, possessing extremely intersting mathematical properties. We present an asymptotic estimate R(\rm as)(r;z≫1) for the function R(r;z) with large arguments z, along with similar formulas for its logarithm and logarithmic derivative. These functions exhibit very interesting oscillatory behavior around their asymptotics, for parameters r above some threshold value r^*. Some implications of our findings are discussed in the context of the Curie-Weiss cell model of simple fluids.