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The work of Hugo Duminil-Copin
Full text linkThis article is an account of the scientific work of Hugo Duminil-Copin at
the time of his award in 2022 of the Fields Medal "for solving longstanding
problems in the probabilistic theory of phase transitions in statistical
physics, especially in dimensions three and four''
The work of Hugo Duminil-Copin
Full text linkThe past decade has seen tremendous progress in our understanding of the
behaviour of many probabilistic models at or near their "critical point". On
the 5th of July 2022, Hugo Duminil-Copin was awarded the Fields medal for the
crucial role he played in many of these developments. In this short review
article, we will try to put his work into context and present a small selection
of his results
The work of Hugo Duminil-Copin
No full textThe past decade has seen tremendous progress in our understanding of the behaviour of many probabilistic models at or near their "critical point". On the 5th of July 2022, Hugo Duminil-Copin was awarded the Fields medal for the crucial role he played in many of these developments. In this short review article, we will try to put his work into context and present a small selection of his results.PROPD
Discrete complex analysis and probability
No full textWe discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo Duminil-Copin and Clément Hongler
Cálculo exato do ponto crítico de modelos de aglomerados aleatórios (q ≥ 1) sobre a rede bidimensional
Full text linkDissertação(mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2013.Este trabalho está baseado no artigo: The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1, escrito pelos matemáticos Vincent Beffara e Hugo Duminil-Copin publicado no periódico Probability Theory and Related Fields em 2012. Neste trabalho os autores provam uma conjectura bastante antiga sobre o valor do ponto crítico do Modelo de Aglomerados Aleatórios na rede Z2. Eles mostraram que o ponto auto-dual, psd(q) = √q /(1 + √q ); para q ≥ 1 é crítico na rede quadrada. Como uma aplicação deste resultado, eles mostraram também que as funções de conectividade, na fase subcrítica, decaem exponencialmente com respeito à distância entre dois pontos. _______________________________________________________________________________________ ABSTRACTThis work is based on the paper: The self-dual point of the two-dimensional randomcluster model is critical for, q ≥ 1, by Vincent Beffara and Hugo Duminil-Copin, Probability Theory and Related Fields 2012. In this work the authors proved an old conjecture about the critical point of the Random-Cluster Model in the square lattice. They shown that the self dual point, psd(q) = √q /(1 + √q ); for q ≥ 1 is critical on the square lattice. As an application they shown that the connectivity functions, in the subcritical phase, decays exponentially fast with the distance of the points.Instituto de Ciências Exatas (IE)Departamento de Matemática (IE MAT)Programa de Pós-Graduação em Matemátic
Correction to: A New Proof of the Sharpness of the Phase Transition for Bernoulli Percolation and the Ising Model
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