Related papers: The work of Hugo Duminil-Copin
The 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…
This is a popular article about the work of Hugo Duminil-Copin, 2022 Fields medalist.
The 2016 Physics Nobel Prize honors a variety of discoveries related to topological phases and phase transitions. Here we sketch two exciting facets: the groundbreaking works by John Kosterlitz and David Thouless on phase transitions of…
Despite the huge amount of literature on h-index, few papers have been devoted to the statistical analysis of h-index when a probabilistic distribution is assumed for citation counts. The present contribution relies on showing the available…
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
Andrei Okounkov received the Fields Medal at the ICM 2006 in Madrid "for his contributions bridging probability, representation theory and algebraic geometry". This is a brief account of his work.
The Nobel Prize in Physics 2021 was awarded to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi for their 'groundbreaking contributions to our understanding of complex systems' including major advances in the understanding of our…
This article is a personal overview of the work of Dennis Sullivan who was awarded the 2022 Abel prize. It was commissioned by the Bulletin of the (Indian) Mathematics Consortium, and it will appear there.
Michel Talagrand (Centre National de la Recherche Scientifique, France) has been awarded the prestigious Abel Prize for 2024 for his work in probability theory, functional analysis, and statistical physics. In this note, we introduce the…
On the occasion of Elliott Lieb being awarded the Gauss Prize 2022, we give a non-technical overview over some of his seminal works in mathematical physics. We emphasize, in particular, his work on Coulomb many-body systems and functional…
In this paper, we show a new relation between phase transition in one-dimensional Statistical Mechanics and the multiplicity of the dimension of the space of harmonic functions for an extension of the classical transfer operator. We…
The 2024 Nobel Prize in Physics was awarded to John Hopfield and Geoffrey Hinton, "for foundational discoveries and inventions that enable machine learning with artificial neural networks." As noted by the Nobel committee, their work moved…
In this paper we suggest a theoretical method based on the statistical mechanics for treating the alpha-helix-random coil transition in alanine polypeptides. We consider this process as a first-order phase transition and develop a theory…
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
The field theoretical approach to duality in the superconducting phase transition is reviewed. Emphasis is given to the scaling behavior, and recent results are discussed.
We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees.
After surveying the quantum kinematics and dynamics of statistical transmutation, I show how this concept suggests a phase diagram for the two-dimensional matter in a magnetic field, as a function of quantum statistics. I discuss the…
The Nobel Prize in Physics 2025 has been awarded to John Clarke, John Martinis, and Michel Devoret for "the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit". Their achievements open up…