arXiv subjects

Hironobu Sakagawa

Publications and source records attributed to Hironobu Sakagawa.

3 recordsLinked to original sources

arXiv2026

Convergence of stationary distributions for a class of zero-range processes and its application to a wealth distribution model with debt

Understanding how macroscopic wealth distributions emerge from microscopic transaction rules among agents is a central problem in econophysics. While many traditional models restrict agents' wealth to non-negative values, debt is an essential feature of realistic economic systems. In this paper, we introduce a stochastic transaction mechanism into the agent-based model with a central-bank-mediated collective debt limit, as studied in [14]. In our model, each agent probabilistically determines whether to transfer a coin, depending on their current asset or debt level. From a probabilistic perspective, the resulting system can be formulated as a zero-range process with $\mathbb{Z}$-valued site occupation numbers, where negative values represent debt. We prove that, under an appropriate scaling, the wealth distribution in the stationary state converges to either a two-sided Gamma distribution or a Gamma distribution, depending on the asymptotic behavior of the function governing coin transfers. Our results rigorously identify these previously unconsidered limiting distributions and provide a mathematical framework for understanding how stochastic monetary exchanges give rise to macroscopic wealth distributions.

math.PR↗

arXiv2025

Limiting distributions of generalized money exchange models

The "Money Exchange Model" is a type of agent-based simulation model used to study how wealth distribution and inequality evolve through monetary exchanges between individuals. The primary focus of this model is to identify the limiting wealth distributions that emerge at the macroscopic level, given the microscopic rules governing the exchanges among agents. In this paper, we formulate generalized versions of the immediate exchange model and the uniform saving model both of which are types of money exchange models, as discrete-time interacting particle systems and characterize their stationary distributions. Furthermore, we prove that under appropriate scaling, the asymptotic wealth distribution converges to a Gamma distribution or an exponential distribution for both models. The limiting distribution depends on the weight function that affects the probability distribution of the number of coins exchanged by each agent. In particular, our results provide a mathematically rigorous formulation and generalization of the assertions previously predicted in studies based on numerical simulations and heuristic arguments.

math.PR↗

arXiv2024

Maximum of the Gaussian interface model in random external fields

We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on $\mathbb{R}^{Λ_N}$, $Λ_N=[-N, N]^d\cap \mathbb{Z}^d$ with Hamiltonian $H_N(ϕ)= \frac{1}{4d}\sum\limits_{x\sim y}(ϕ(x)-ϕ(y))^2-\sum\limits_{x\in Λ_N}η(x)ϕ(x)$ and $0$-boundary conditions. $\{η(x)\}_{x\in \mathbb{Z}^d}$ is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable $η(x)$ when $d\geq 5$. In particular, we identify the leading order asymptotics of the maximum.

math.PR↗