Related papers: The Derrida--Retaux conjecture on recursive models
We analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of N coupled two-dimensional Ising models. For N>2 the pure model exhibits a fluctuation-driven first order transition,…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite…
The ground state of the quantum rotor model in two dimensions with random phase frustration is investigated. Extensive Monte Carlo simulations are performed on the corresponding (2+1)-dimensional classical model under the entropic sampling…
We perfect the recursion-transform method to be a complete theory, which can derive the general exact resistance between any two nodes in a resistor network with several arbitrary boundaries. As application of the method, we give a profound…
In this paper, based on lectures by the authors at the May 2015 workshop {\it Resurgence, Physics and Numbers}, at the Centro di Ricerca Matematica Ennio De Giorgio of the Scuola Normale Superiore in Pisa, we explain the origin of resurgent…
While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less in known about critical points of the corresponding energy. Saddle…
We are interested in the random walk in random environment on an infinite tree. Lyons and Pemantle [11] give a precise recurrence/transience criterion. Our paper focuses on the almost sure asymptotic behaviours of a recurrent random walk…
This work extends the thermodynamic analysis of random bond percolation to explosive and hybrid percolation models. We show that this thermodynamic analysis is well applicable to both explosive and hybrid percolation models by using the…
We prove the validity of the freeness conjecture of Brou\'e, Malle and Rouquier for the generic Hecke algebras associated to the exceptional complex reflection groups of rank 2 belonging to the tetrahedral and octahedral families, and we…
We propose a variation of the GMS model of evolution of species. In this version, as in the GMS model, at each birth, the new species in the system is labeled with a random fitness mark, but in our variation, to each extinction event is…
We show that induction over $\Delta(\mathbb R)$-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The…
We analyze from the renormalization group perspective a universality class of reaction-diffusion systems with absorbing states. It describes models where the vacuum state is not accessible, as the set of reactions $2 A \to A$ together with…
The second law of thermodynamics states that entropy production in macroscopic systems is non-negative, reaching zero only at thermodynamic equilibrium. As a corollary, this implies that the state trajectory of macroscopic systems is…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
We establish a super-replication duality in a continuous-time financial model where an investor's trades adversely affect bid- and ask-prices for a risky asset and where market resilience drives the resulting spread back towards zero at an…
The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the…
The free energies of six-vertex models on general domain D with various boundary conditions are investigated with the use of the n-equivalence relation which classifies the thermodynamic limit properties. It is derived that the free energy…
We consider disordered pinning models, when the return time distribution of the underlying renewal process has a polynomial tail with exponent $\alpha \in (1/2,1)$. This corresponds to a regime where disorder is known to be relevant, i.e.…
Confinement indicates an asymptotic quark state not observable except its energy is zero. Unitarity indicates that the total probability of a definite state of quark system to transit to any final state is exactly one. This talk reviews…