Related papers: Un-inverting the Parisi formula
We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem,…
We prove an upper bound for the free energy (per unit volume) of the dilute Bose gas in the thermodynamic limit, showing that the free energy at density $\rho$ and inverse temperature $\beta$ differs from that of the non-interacting system…
The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having…
We investigate the behavior of the rare fluctuations of the free energy in the p-spin spherical model, evaluating the corresponding rate function via the G\"artner-Ellis theorem. This approach requires the knowledge of the analytic…
Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fields which are weakly dependent in the sense of Lewis,…
In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…
We analyse the critical region of finite-($d$)-dimensional Ising spin glass, in particular the limit of $d$ closely above the lower critical dimension $d_\ell$. At criticality the thermally active degrees of freedom are surfaces (of width…
In scattering theory, the unitary limit is defined by an infinite scattering-length and a zero effective range, corresponding to a phase-shift \pi/2, independent of energy. This condition is satisfied by a rank-1 separable potential…
At sufficiently low temperatures, the configurational phase space of a large spin-glass system breaks into many separated domains, each of which is referred to as a macroscopic state. The system is able to visit all spin configurations of…
We propose a method to bound the expectation of the supremum of the price process in stochastic volatility models. It can be applied, for example, to the rough Bergomi model, avoiding the need to discuss finiteness of higher moments. Our…
Entropy functions played a key role in the development of mathematical theory for hyperbolic conservation laws. The notion of entropy, which is intimately connected with symmetry, is an extension \emph{imposed} on nonlinear systems of…
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…
We discuss a generalization of the conditions of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $L^2$ metric structure of the Gaussian…
Tropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann constant k going to 0 is discussed. It is shown that such tropical limit is well-adapted to analyse properties of systems with highly degenerated…
This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how…
The Renyi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Renyi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide…
We introduce the concept of Random Multi-Overlap Structures in diluted spin glasses, following the ideas of Aizenman, Sims and Starr for non-diluted models. As a result, we prove the generalized bound and variational principle for the free…
We study the free energy of mixed $p$-spin spin glass models enriched with an additional magnetic field given by the canonical Gaussian field associated with a Ruelle probability cascade. We prove that this free energy converges to the…
The usual approaches to the definition of energy give an ambiguous result for the energy of fields in the radiating regime. We show that for a massless scalar field in Minkowski space-time the definition may be rendered unambiguous by…
An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite…