Why we think this paper is great for you:
This paper directly investigates the mechanisms that amplify wealth inequality, offering you a deep dive into the economic dynamics driving disparities.

Abstract
This paper investigates the emergence of wealth inequality through a minimalist kinetic exchange model that incorporates two fundamental economic features: fixed-amount transactions and hard budget constraints. In contrast to the maximum entropy principle, which predicts an exponential Boltzmann-Gibbs distribution with moderate inequality for unconstrained wealth exchange, we demonstrate that these realistic trading rules drive the system toward a highly unequal steady state. We develop a self-consistent mean-field theory, deriving a master equation where agent income follows a Poisson process coupled to the poverty rate. Numerical solution reveals a stationary distribution characterized by a substantial pauper class, high Gini coefficient, and exponential tail--significantly deviating from the maximum entropy benchmark. Agent-based simulations confirm these findings. We identify the poverty trap as the key mechanism: the liquidity constraint creates asymmetric economic agency, where zero-wealth agents become passive recipients, unable to participate in wealth circulation. This work establishes that substantial inequality can emerge spontaneously from equal-opportunity exchanges under basic economic constraints, without requiring agent heterogeneity or multiplicative advantage, providing a mechanistic foundation for understanding poverty as an emergent property of exchange rules.

AI Summary

• The maximum entropy principle, yielding the Boltzmann-Gibbs distribution, serves as a fundamental "natural scale" for inequality from pure randomness, and deviations highlight the profound impact of specific microscopic exchange rules. [3]
• The developed framework serves as a quantitative test-bed for evaluating fiscal policies, such as basic income or targeted welfare, to assess their efficacy in reducing inequality and poverty. [3]
• Fixed-amount transactions and hard budget constraints spontaneously generate a "poverty trap" and significantly amplify wealth inequality (Gini ≈0.65) compared to the maximum entropy benchmark (Gini ≈0.33). [2]
• The "poverty trap" mechanism arises from asymmetric economic agency, where zero-wealth agents become passive recipients unable to initiate transactions, coupled with a mean income insufficient to cover mandatory expenditures for active agents. [2]
• Substantial wealth inequality, including a large pauper class (p0 ≈41-55%), can emerge from equal-opportunity, stochastic exchanges without requiring agent heterogeneity, multiplicative advantage, or strategic behavior. [2]
• The model provides a mechanistic, bottom-up explanation for poverty as an emergent property of exchange rules, translating the economic concept of a poverty trap into precise statistical dynamics. [2]
• The dynamical constraints imposed by fixed transactions and liquidity rules restrict the accessible state space, leading to a stationary distribution that fundamentally differs from the global maximum entropy solution. [2]
• Fixed-Amount Transactions: A rule where active agents must send a fixed payment of exactly 1 unit of wealth, differing from fractional or randomly varying transaction amounts. [2]
• Hard Budget Constraint (Liquidity Constraint): The rule that an agent cannot spend what they do not have, specifically meaning agents with zero wealth cannot make payments. [2]
• Maximum Entropy Principle: A principle stating that the probability distribution best representing current knowledge, constrained by conserved quantities (e.g., total wealth), is the one with the largest Shannon entropy. [2]

Why we think this paper is great for you:
You will find this paper highly relevant as it examines how school choice policies contribute to wealth segregation, a significant aspect of social and economic inequality.

Abstract
We study how school choice mechanisms shape wealth segregation in the long term by endogenizing residential choice. Families buy houses in school zones that determine admission priority, experience shocks to school preferences, and participate in one of three mechanisms: neighborhood assignment (N), Deferred Acceptance (DA), or Top Trading Cycles (TTC). Neighborhood segregation increases from N to DA to TTC. DA and TTC reduce school-level segregation relative to neighborhoods but typically not enough to reverse this ranking, and housing prices in oversubscribed zones rise in the same order. Two desegregation policies further illustrate how short- and long-term perspectives can differ.

Why we think this paper is great for you:
This paper explores the challenges of fair resource allocation and its social impact, which aligns well with your interest in the broader implications of inequality.

Abstract
In standard fair division models, we assume that all agents are selfish. However, in many scenarios, division of resources has a direct impact on the whole group or even society. Therefore, we study fair allocations of indivisible items that, at the same time, maximize social impact. In this model, each agent is associated with two additive functions that define their value and social impact for each item. The goal is to allocate items so that the social impact is maximized while maintaining some fairness criterion. We reveal that the complexity of the problem heavily depends on whether the agents are socially aware, i.e., they take into consideration the social impact functions. For socially unaware agents, we prove that the problem is NP-hard for a variety of fairness notions, and that it is tractable only for very restricted cases, e.g., if, for every agent, the valuation equals social impact and it is binary. On the other hand, social awareness allows for fair allocations that maximize social impact, and such allocations can be computed in polynomial time. Interestingly, the problem becomes again intractable as soon as the definition of social awareness is relaxed.

Why we think this paper is great for you:
This paper directly investigates the mechanisms that amplify wealth inequality, offering you a deep dive into the economic dynamics driving disparities.

Abstract
This paper investigates the emergence of wealth inequality through a minimalist kinetic exchange model that incorporates two fundamental economic features: fixed-amount transactions and hard budget constraints. In contrast to the maximum entropy principle, which predicts an exponential Boltzmann-Gibbs distribution with moderate inequality for unconstrained wealth exchange, we demonstrate that these realistic trading rules drive the system toward a highly unequal steady state. We develop a self-consistent mean-field theory, deriving a master equation where agent income follows a Poisson process coupled to the poverty rate. Numerical solution reveals a stationary distribution characterized by a substantial pauper class, high Gini coefficient, and exponential tail--significantly deviating from the maximum entropy benchmark. Agent-based simulations confirm these findings. We identify the poverty trap as the key mechanism: the liquidity constraint creates asymmetric economic agency, where zero-wealth agents become passive recipients, unable to participate in wealth circulation. This work establishes that substantial inequality can emerge spontaneously from equal-opportunity exchanges under basic economic constraints, without requiring agent heterogeneity or multiplicative advantage, providing a mechanistic foundation for understanding poverty as an emergent property of exchange rules.

AI Summary

• The maximum entropy principle, yielding the Boltzmann-Gibbs distribution, serves as a fundamental "natural scale" for inequality from pure randomness, and deviations highlight the profound impact of specific microscopic exchange rules. [3]
• The developed framework serves as a quantitative test-bed for evaluating fiscal policies, such as basic income or targeted welfare, to assess their efficacy in reducing inequality and poverty. [3]
• Fixed-amount transactions and hard budget constraints spontaneously generate a "poverty trap" and significantly amplify wealth inequality (Gini ≈0.65) compared to the maximum entropy benchmark (Gini ≈0.33). [2]
• The "poverty trap" mechanism arises from asymmetric economic agency, where zero-wealth agents become passive recipients unable to initiate transactions, coupled with a mean income insufficient to cover mandatory expenditures for active agents. [2]
• Substantial wealth inequality, including a large pauper class (p0 ≈41-55%), can emerge from equal-opportunity, stochastic exchanges without requiring agent heterogeneity, multiplicative advantage, or strategic behavior. [2]
• The model provides a mechanistic, bottom-up explanation for poverty as an emergent property of exchange rules, translating the economic concept of a poverty trap into precise statistical dynamics. [2]
• The dynamical constraints imposed by fixed transactions and liquidity rules restrict the accessible state space, leading to a stationary distribution that fundamentally differs from the global maximum entropy solution. [2]
• Fixed-Amount Transactions: A rule where active agents must send a fixed payment of exactly 1 unit of wealth, differing from fractional or randomly varying transaction amounts. [2]
• Hard Budget Constraint (Liquidity Constraint): The rule that an agent cannot spend what they do not have, specifically meaning agents with zero wealth cannot make payments. [2]
• Maximum Entropy Principle: A principle stating that the probability distribution best representing current knowledge, constrained by conserved quantities (e.g., total wealth), is the one with the largest Shannon entropy. [2]

Why we think this paper is great for you:
You will find this paper highly relevant as it examines how school choice policies contribute to wealth segregation, a significant aspect of social and economic inequality.

Abstract
We study how school choice mechanisms shape wealth segregation in the long term by endogenizing residential choice. Families buy houses in school zones that determine admission priority, experience shocks to school preferences, and participate in one of three mechanisms: neighborhood assignment (N), Deferred Acceptance (DA), or Top Trading Cycles (TTC). Neighborhood segregation increases from N to DA to TTC. DA and TTC reduce school-level segregation relative to neighborhoods but typically not enough to reverse this ranking, and housing prices in oversubscribed zones rise in the same order. Two desegregation policies further illustrate how short- and long-term perspectives can differ.

Why we think this paper is great for you:
While not directly related to your core interests, this paper explores advanced mathematical inequalities that might be of interest if you have a secondary focus on theoretical mathematics.

Abstract
Two types of Bernstein inequalities are established on the unit ball in $\mathbb{R}^d$, which are stronger than those known in the literature. The first type consists of inequalities in $L^p$ norm for a fully symmetric doubling weight on the unit ball. The second type consists of sharp inequalities in $L^2$ norm for the Jacobi weight, which are established via a new self-adjoint form of the spectral operator that has orthogonal polynomials as eigenfunctions.

Why we think this paper is great for you:
This paper presents a unified mathematical approach to Hardy-type inequalities, which could be relevant if you are exploring the theoretical underpinnings of certain analytical models.

Abstract
In this paper, we provide suitable characterisations of pairs of weights $(V,W),$ known as Bessel pairs, that ensure the validity of weighted Hardy-type inequalities. The abstract approach adopted here makes it possible to establish such inequalities also going beyond the classical Euclidean setting and also within a more general $L^p$ framework. As a byproduct of our method, we obtain explicit expressions for the maximizing functions and, in certain specific situations, we show that the associated constants are sharp. We emphasise that our approach unifies, generalises and improves several existing results in the literature.