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math.AP2025
The Bennati-Dragulescu-Yakovenko model in the continuous setting: PDE derivation and long-time behavior
Fei Cao, Nadia Loy
In this manuscript, we develop and analyze a continuous version of the well-known Bennati-Dragulescu-Yakovenko (BDY) dollar-exchange discrete model. Starting from the conservative…
math.PR2025
Mean-field analysis of a random asset exchange model with probabilistic cheaters
Fei Cao
We investigate a variant of the standard Bennati-Dragulescu-Yakovenko (BDY) game \cite{dragulescu_statistical_2000} inspired by the very recent work \cite{blom_hallmarks_2024}, whe…
math.PR2025
Generative diffusion models from a PDE perspective
Fei Cao, Kimball Johnston, Thomas Laurent +2
Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of th…