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math.PR2025
Decoupling the i.i.d. field and the randomisation field in the Curie-Weiss model
Yacine Barhoumi-Andréani, Peter Eichelsbacher
Using the De Finetti representation of the Curie-Weiss model, the uniform coupling of Bernoulli random variables and the Laplace inversion formula (almost surely), we show that the…
math.PR2025
Splitting phenomenon in the Sathe-Selberg theorem, mod-Poisson convergence with auxiliary randomisation and universality of the Gamma factor
Yacine Barhoumi-Andréani
We consider several sequences of random variables whose Fourier-Laplace transforms present the same type of \textit{splitting phenomenon} when suitably rescaled by the Fourier-Lapl…
math.PR2024
Remarkable structures in integrable probability, I: max-independence structures
Yacine Barhoumi-Andréani
We analyse in a systematic way the occurrences of a remarkable structure in the theory of integrable probability that we call a ``max-independence structure'', when random variable…