This paper studies an interacting particle system of interest in econophysics inspired from a model introduced in the physics literature. The original model consists of the customers of a single bank characterized by their capital, and the discrete-time dynamics consists of monetary transactions in which a random individual x gives one coin to another random individual y, the transaction being canceled when x is in debt and there is no more coins to borrow from the bank. Using a combination of numerical simulations and heuristic arguments, physicists conjectured that the distribution of money (the distribution of the number of coins owned by a given individual) at equilibrium converges to an asymmetric Laplace distribution in the large population/temperature limit. In this paper, we prove and extend this conjecture to a more general model including multiple banks and interactions among customers across banks. More importantly, our model assumes that customers are located on a general undirected connected graph (as opposed to the complete graph in the original model) where neighbors are interpreted as business partners, and transactions occur along the edges, thus modeling the flow of money across a social network. We show the convergence to the asymmetric Laplace distribution in the large population/temperature limit for any graph, thus proving and extending the conjecture from the physicists, and derive an exact expression of the distribution of money for all population sizes and money temperatures. * Nicolas Lanchier was partially supported by NSF grant CNS-2000792.
With this chapter, the author sheds light on the experiences of a Black woman hired to create, administer, and manage the day-to-day needs of diversity offices at two small, white private liberal arts universities. The chapter will include insights on the very racism and implicit bias the author experienced, reported, and helped diminish. The chapter also describes the seemingly impossible task of managing change and transformation on private institutions rooted in white supremacist traditions and built upon a history of exclusion. To do this, the author shares personal narratives from colleagues collected via online surveys. The author describes the personal angst experienced while collecting, reporting, and managing the many micro-aggressions, experiences with racism, transphobia, and other reported biases. The author considers the mental gymnastics necessary to serve the needs of the institution and attempt to protect personal integrity and sanity.
The UK government's Prevent programme affects professionals and the people who rely on their services across the public sector, particularly now that workers are legally bound to report their concerns about individuals they believe to be at risk of radicalisation. This article discusses the risks that the strategy presents to the work of teachers and the bonds of trusts between staff and students.
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