Related papers: Remarks Concerning Polyakov's Conjecture for the 3…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…
We study the 3D Ising model in the infinite volume limit $N_{x,y,z}\to\infty$ by means of numerical simulations. We determine $T_c$ as well as the critical exponents $\beta,\gamma$ and $\nu$, based on finite-size scaling and histogram…
We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial…
We provide a theoretical analysis by means of the nonperturbative functional renormalization group (NP-FRG) of the corrections to scaling in the critical behavior of the random-field Ising model (RFIM) near the dimension $d_{DR}\approx 5.1$…
In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…
String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is…
We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…
We report precise simulations of phi^4 theory in the Ising limit. A recent technique to stochastically evaluate the all-order strong coupling expansion is combined with exact identities in the closely related Aizenman random current…
We study products of arbitrary random real $2 \times 2$ matrices that are close to the identity matrix. Using the Iwasawa decomposition of $\text{SL}(2,{\mathbb R})$, we identify a continuum regime where the mean values and the covariances…
We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of any given node is estimated by…
A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to…
Mixed level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao and Gilbert-Varshamov type bounds for mixed level orthogonal arrays. The computational complexity of the terms involved…
The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by Monte-Carlo simulations. Within the Ising universality class constraints lead to Fisher…
Using polynomial truncations of the Fourier transform of the RG transformation of Dyson's hierarchical model, we show that it is possible to calculate very accurately the renormalized quantities in the symmetric phase. Numerical results…
By considering the renormalization group flow between $N$ coupled Ising models in the UV and the cubic fixed point in the IR, we study the large $N$ behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion…
We present a setup that enables to define in a concrete way a renormalization flow for the FK-percolation models from statistical physics (that are closely related to Ising and Potts models). In this setting that is applicable in any…
We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on…
We perform stability analyses for discontinuous Galerkin spectral element approximations of linear variable coefficient hyperbolic systems in three dimensional domains with curved elements. Although high order, the precision of the…
We prove a Korovkin type approximation theorem via power series methods of summability for continuous $2\pi$-periodic functions of two variables and verify the convergence of approximating double sequences of positive linear operators by…