Related papers: New probabilistic methods for physics
We present how a probabilistic model can describe the asymptotic behaviour of the iterations, especially for ODE with an approach of the Poincar\'e-Bendixon's problem in $\mathbb{R}^d$. On pr\'esente un mod\`ele probabiliste pour d\'ecrire…
We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject. Among the applications, we use new methods to compute…
First approach of invariant densities of a Perron Frobenius operator. Asymptotic behaviours of ODE or PDE, as, are most interesting. The associed infinitesimal iteration is. If is partially linear, a random distribution can be asymptotic…
We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…
We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
We show that the asymptotic iteration method converges and yields accurate energies for a perturbed Coulomb model. We also discuss alternative perturbation approaches to that model.
We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…
This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial…
In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…
This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…
We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…
We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does…
Self-interacting diffusions are solutions to SDEs with a drift term depending on the process and its normalized occupation measure $\mu_t$ (via an interaction potential and a confinement potential). We establish a relation between the…
The question about asymptotical behaviour of solutions for the system $\dot x=A_\nu x+f$ for big values of the parameter $\nu\in\frak A$ is considered. An approach to the reduction of a large class of problems to easily solvable problem…