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arXiv · 2105.10321

L'invariance conforme et l'universalité au point critique des modèles bidimensionnels

Yvan Saint-Aubin
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Abstract

Résumé. Des quelques articles publiés par Robert P. Langlands en physique mathématique, c'est celui publié dans le {\it Bulletin of the American Mathematical Society} sous le titre {\it Conformal invariance in two-dimensional percolation} qui a eu, à ce jour, le plus d'impact : les idées d'Oded Schramm ayant mené à l'équation de Loewner stochastique et les preuves de l'invariance conforme de modèles de physique statistique par Stanislav Smirnov ont été suscitées, au moins en partie, par cet article. Ce chapitre rappelle sommairement quelques idées de l'article original ainsi que celles issues des travaux de Schramm et Smirnov. Il est aussi l'occasion pour moi de décrire la naissance de ma collaboration avec Robert Langlands et d'exprimer ma profonde gratitude pour cette fantastique expérience scientifique et humaine. Abstract. Of all mathematical physics contributions by Robert P. Langlands, the paper {\it Conformal invariance in two-dimensional percolation} published in the {\it Bulletin of the American Mathematical Society} is the one that has had, up to now, the most significant impact: Oded Schramm's ideas leading to the stocastic Loewner equation and Stanislav Smirnov's proof in two dimensions were at least partially inspired by it. This chapter reviews briefly some ideas of the original paper and some of those by Schramm and Smirnov.

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Yvan Saint-Aubin. 2021-05-21. L'invariance conforme et l'universalité au point critique des modèles bidimensionnels. https://doi.org/10.1017/9781108591218

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