Related papers: The Derrida--Retaux conjecture on recursive models

We revisit the proof of the limiting free energy of the continuous random energy model (CREM) using the Hamilton--Jacobi approach for mean-field disordered systems. To achieve this, we introduce an enriched model that interpolates between…

We study and generalize in various ways the model of rational expectation (RE) bubbles introduced by Blanchard and Watson in the economic literature. First, bubbles are argued to be the equivalent of Goldstone modes of the fundamental…

Using inverse Ising inference we show that the absorbing states of the one-dimensional Manna model can be described by an equilibrium model with an emergent interaction displaying short-ranged repulsion and long-ranged attraction. As the…

We study the free energy for pure and mixed spherical $p$-spin models with i.i.d.\ disorder. In the mixed case, each $p$-interaction layer is assumed either to have regularly varying tails with exponent $\alpha_p$ or to satisfy a finite…

In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…

In this paper, we consider a stochastic recursive optimal control problem under model uncertainty. In this framework, the cost function is described by solutions of a family of backward stochastic differential equations. With the help of…

For real-valued additive process $(X\_t)\_{t\geq 0}$ a recursive equation is derived for the entire positive moments of functionals $$I\_{s,t}= \int \_s^t\exp(-X\_u)du, \quad 0\leq s<t\leq\infty, $$ in case the Laplace exponent of $X\_t$…

We investigate supereigenvalue models in the Ramond sector and their recursive structure. We prove that the free energy truncates at quadratic order in Grassmann coupling constants, and consider super loop equations of the models with the…

We consider a class of cross diffusion systems with degenerate (or porous media type) diffusion which is inspired by models in mathematical biology/ecology with zero self diffusions. Known techniques for scalar equations are no longer…

The world of primes has many gaps between evidence and theorems. Here, we review Legendre's conjecture on primes between consecutive squares and recent progress on the weaker question of primes between consecutive larger powers. Assuming…

We consider a particular weak disorder limit ("continuum limit") of matrix products that arise in the analysis of disordered statistical mechanics systems, with a particular focus on random transfer matrices. The limit system is a diffusion…

We provide some on-off type criteria for recurrence and transience of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion…

We consider a class of abstract second order evolution equations with a restoring force that is strictly superlinear at infinity with respect to the position, and a dissipation mechanism that is strictly superlinear at infinity with respect…

We study how the Einstein relation between spontaneous fluctuations and the response to an external perturbation holds in the absence of currents, for the comb model and the elastic single-file, which are examples of systems with…

We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate…

The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions is proved. The cross-diffusion part describes the…

We consider Fujita's freeness conjecture in a relative setting and prove a criterion by proving a correct Q-divisor version of the Kollar vanishing theorem.

We study existence, uniqueness and computability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences---one that analyzes principal eigenvalues of…

One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two…

The current research on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite…