We give a proof of the replica symmetric formula for the free energy of the Sherrington-Kirkpatrick model in high temperature which is based on the TAP formula. This is achieved by showing that...
Publications
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Friday, 21 September, 2018
arXiv:1809.07972
Tuesday, 18 September, 2018
We propose a cosmological scenario involving a single scalar field, \varphi, that is a source of Dark Matter as well as Dark Energy. The Lagrangian density of \varphi contains a second field \...
arXiv:1809.07409
Tuesday, 18 September, 2018
We describe new graphical models of the framed little disks operads which exhibit large symmetry dg Lie algebras.
arXiv:1809.06918
Monday, 17 September, 2018
In this note, we perform the large-charge expansion for non-relativistic systems with a global U(1) symmetry in 3+1 and 2+1 space-time dimensions, motivated by applications to the unitary Fermi...
arXiv:1809.06371
Friday, 14 September, 2018
In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased...
arXiv:1809.05537
Sunday, 9 September, 2018
The aim of this note is to review some recent developments on the regularity theory for the stationary and parabolic obstacle problems. After a general overview, we present some recent results...
arXiv:1809.02932
Thursday, 6 September, 2018
While Hartree-Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In...
arXiv:1809.01902
Thursday, 6 September, 2018
We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of m^2=n^2+nl+l^2.
arXiv:1809.02037
Tuesday, 4 September, 2018
Let c_n = c_n(d) denote the number of self-avoiding walks of length n starting at the origin in the Euclidean nearest-neighbour lattice \mathbb{Z}^d. Let \mu = \lim_n c_n^{1/n} denote the...
arXiv:1809.00760
Monday, 3 September, 2018
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a...
arXiv:1809.00516
Wednesday, 29 August, 2018
Given a real function f on an interval [a,b] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f,f′ and f...
arXiv:1808.09690
Tuesday, 28 August, 2018
We prove a local law for the adjacency matrix of the Erd\H{o}s-R\'enyi graph G(N,p) in the supercritical regime pN \geq C\log N where G(N,p) has with high probability no isolated vertices. In...
arXiv:1808.09437