3,226 research outputs found
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
Hugo DUMINIL-COPIN - Critical phenomena through the lens of the Ising model: AMS-EMS-SMF International meeting 2022
No full textThe Ising model is one of the most classical lattice models of statistical physics undergoing a phase transition. Initially imagined as a model for ferromagnetism, it revealed itself as a very rich mathematical object and a powerful theoretical tool to understand cooperative phenomena. Over one hundred years of its history, a profound understanding of its critical phase has been obtained. While integrability and mean-field behavior led to extraordinary breakthroughs in the two-dimensional and high-dimensional cases respectively, the model in three and four dimensions remained mysterious for years. In this talk, we will present recent progress in these dimensions based on a probabilistic interpretation of the Ising model relating it to percolation models
The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1
No full textAbstract. In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nien-huis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a honeycomb) lattice is µ
Recommended from our members
Dimerization and Néel Order in Different Quantum Spin Chains Through a Shared Loop Representation
No full textThe ground-states of the spin-S antiferromagnetic chain HAF with a projection-based interaction and the spin-1/2 XXZ-chain HXXZ at anisotropy parameter Δ = cosh(λ) share a common loop representation
in terms of a two-dimensional functional integral which is similar to the classical planar Q-state Potts model at √Q = 2S + 1 = 2 cosh(λ). The multifaceted relation is used here to directly relate the distinct forms of
translation symmetry breaking which are manifested in the ground-states of these two models: dimerization for HAF at all S > 1/2, and Neel order for HXXZ at λ > 0. The results presented include: (i) a translation to the above quantum spin systems of the results which were recently proven by Duminil–Copin–Li–Manolescu for a broad class of two-dimensional random-cluster models, and (ii) a short proof of the symmetry breaking in a manner similar to the recent structural proof by Ray–Spinka of the discontinuity of the phase transition for Q > 4. Altogether, the quantum manifestation of the change between Q = 4 and Q > 4 is a transition from a gapless ground-state to a pair of gapped and extensively distinct ground-states
Conformal invariance of double random currents I: Identification of the limit
Full text linkThis is the first of two papers devoted to the proof of conformal invariance of the critical double random current model on the square lattice. More precisely, we show the convergence of loop ensembles obtained by taking the cluster boundaries in the sum of two independent currents with free and wired boundary conditions. The strategy is first to prove convergence of the associated height function to the continuum Gaussian free field, and then to characterise the scaling limit of the loop ensembles as certain local sets of this Gaussian free field. In this paper, we identify uniquely the possible subsequential limits of the loop ensembles. Combined with Duminil-Copin et al., this completes the proof of conformal invariance
Hugo Duminil Copin - Compter les chemins auto-évitants sur le réseau en nid d'abeille: Des mathématiciens primés par l’Académie des Sciences 2017
No full textIHES, Prix Jacques Herbrand 2017 Réalisation technique : Antoine Orlandi (GRICAD) | Tous droits réservé
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
On some aspects of the behaviour of paths and interfaces in discrete and continuous models: random-cluster model, self-repelling polymers and Brownian motion
No full textThis work is composed of three self-contained parts, where the different models of statistical physics are discussed. In Chapter 1 we discuss the random-cluster model. We present another proof of the well-known fact that for square lattice the critical probability of the random-cluster model is equal to for . This proof involves the method of parafermionic observables. In Chapter 3 we study the behaviour of random walks on the square lattice under self-repelling polymers measure. It is a generalisation of a model called self-avoiding walks. We show that, as for self-avoiding walks, self-repelling polymers are sub-ballistic in with , i.e that the probability for the walk to go linearly (on the number of steps) far is exponentially small. In the remaining chapter we look at continuous Brownian motion on different three-dimensional spaces. We compare the behaviour of the Brownian motion in the Euclidian space and in the spaces of constant non-zero curvature. Projections of these distributions under certain moment maps corresponds to the Duistermaat-Heckmann measure
- …
