Recent Progress in Statistical Mechanics
Org:
Vojkan Jakšić (McGill) and
Renaud Raquépas (New York University)
[
PDF]
 NICHOLAS BARNFIELD, McGill University
On the ZivMerhav theorem beyond Markovianity [PDF]

In 1993, Ziv and Merhav proposed a ``new notion of empirical informational divergence'', or relativeentropy estimator which has met great practical application, yet has seen no significant development in the mathematical literature until recently. In this talk, I will compare their algorithm with more conventional universal entropic estimators and discuss a recent generalization of the ZivMerhav Theorem. This extension encompasses a broader class of decoupled measures including the the class of multilevel Markov measures covered by the original result as well as suitably regular gmeasures amongst other examples.
Joint work with R. Grondin, G. Pozzoli, and R. Raquépas.
 LIA BRONSARD, McMaster University
Boundary defects in liquid crystals/ Défauts aux limites dans les cristaux liquides [PDF]

We study the effect of "weak" and "strong" boundary conditions on the location and type of defects observed in a Landau de Gennes thinfilm model for liquid crystals. We study both the minimizers of the associated GinzburgLandau energy as well as the Gamma limit when the correlation length tends to zero. These represent joint works with S. Alama and L. van Brussel, as well as with A. Colinet.
Nous étudions l'effet des conditions aux limites "faibles" et "fortes" sur l'emplacement et le type de défauts observés dans un modèle film mince de Landau de Gennes pour les cristaux liquides. Nous étudions à la fois les minimiseurs de l'énergie de GinzburgLandau associée ainsi que la limite Gamma lorsque la longueur de corrélation tend vers zéro. Il s'agit de travaux conjoints avec S. Alama et L. van Brussel, ainsi qu'avec A. Colinet.
 ALEXANDER FRIBERGH, Université de Montréal
Biased random walks on supercritical percolation clusters [PDF]

We will study the existence, and nonexistence, of scaling limits for the biased random walks on the supercritical percolation cluster in the zerospeed regime.
This is joint work with Alan Hammond.
 RAPHAËL GRONDIN, McGill University
A different approach to the ZivMerhav Theorem [PDF]

This talk will present an almostsure convergence result for a slight modification of the ZivMerhav crossentropy estimator introduced in Nicholas's talk. This result encompasses examples which were not covered by our latest work such as hiddenMarkov measures and unraveling of repeated quantum measurements, satisfying some mild decay assumptions. Our approach is based on the study of a rescaled cumulantgenerating function called the crossentropic pressure, which makes an analogy with the study of large deviations in statistical mechanics.
 ELIAS HESSCHILDS, New York University
Propagation of chaos from the perspective of perturbation theory [PDF]

In this talk, I present my recent work on the meanfield behaviour of diffusions in the torus with bounded pairwise interaction. Using a perturbative expansion of the probability density marginals and iterating inequalities derived from the BBGKY hierarchy, I give sharp higherorder corrections to propagation of chaos. Joint work with Keefer Rowan.
 BENJAMIN LANDON, University of Toronto
Tail estimates for stationary KPZ models [PDF]

The limiting distributions of observables in the KPZ universality class exhibit
tail exponents of $\frac{3}{2}$ and $3$. In this talk we will review recent work
studying the upper tail exponent $\frac{3}{2}$ in the moderate deviations regime of
several KPZ models at finite size, including the stochastic six vertex
model, the ASEP and a class of nonintegrable interacting diffusions.
Joint work with C. Noack and P. Sosoe
 GILLES PAREZ, Université de Montréal
The range of entanglement [PDF]

The investigation of entanglement in quantum manybody systems is a prominent research area, at the intersection of condensed matter, statistical mechanics and quantum information. In particular, quantifying entanglement in quantum critical systems provides us with strong insights regarding universal features of the phase transition. Due to the powerlaw decay of correlations at quantum critical points, it is generally believed that these systems exhibit longrange entanglement between separated regions. In this talk, I will challenge this basic idea by showing that the longdistance entanglement depends greatly on the bosonic or fermionic nature of the model: bosonic theories lack such entanglement, while theories with fermions are substantially more entangled. I will also discuss the generalization of these results to the important case of multipartite systems.
Joint work with W. WitczakKrempa (Université de Montréal), based on arXiv:2310.15273.
 JACOB SHAPIRO, Princeton University
Classification of disordered insulators in 1D [PDF]

In this talk I will describe some of the mathematical aspects of disordered topological insulators. These are novel materials which insulate in their bulk but (may) conduct along their edge; the quintessential example is that of the integer quantum Hall effect. What characterizes these materials is the existence of a topological index, experimentally measurable and macroscopically quantized. Mathematically this is explained by applying algebraic topology to the space of appropriate quantum mechanical Hamiltonians; I will survey some recent results mainly concentrating on the classification problem in one dimension, where the problem reduces to studying spaces of unitaries (resp. orthogonal projections) which essentiallycommute with a fixed projection.
 ISRAEL MICHAEL SIGAL, University of Toronto
Some Rigorous Results on Propagation of Quantum Information [PDF]

In this talk I present some recent results on evolution of quantum correlations and states, and on quantum messaging in general manybody quantum lattice systems. The proofs are derived from a new type of the LiebRobinson bound. The talk based on a joint work with Jérémy Faupin, Marius Lemm and Jingxuan Zhang.
 LUC VINET, IVADO/CRM, Université de Montréal
Entanglement of free fermiom systems, signal processing and algebraic combinatorics [PDF]

Recent advances in the study of the entanglement entropy of free fermions will be presented and their connection with elements of signal processing and algebraic combinatorics will be stressed.
Work done in collaboration with PierreAntoine Bernard, Nicolas Crampé, Rafael Nepomechie, Gilles Parez et al.
© Canadian Mathematical Society