Related papers: Renormalization of random models: a review
In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also…
This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure It\^o and Stratonovich integrals. In the second part, a survey and new results are presented in relation with finite…
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper,…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…
A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.
We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization…
Contents: I. Introduction II. Manifolds in random media III. Thermal fluctuations without disorder IV. Random forces V. Random potential: variational approach VI. Physical interpretation of the solution
The basis of renormalon calculus is briefly discussed. The method is applied to study QCD predictions for three sum rules of deep-inelastic scattering, namely for the Gross-Llewellyn Smith, Bjorken polarized and unpolarized sum rules. It is…
We consider regularity for solutions of a class of de Rham's functional equations. Under some smoothness conditions of functions consisting the equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our results are…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…
A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak $L^\infty$-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness…
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…
In recent years, many papers have been devoted to the regularity of doubly nonlinear singular evolution equations. Many of the proofs are unnecessarily complicated, rely on superfluous assumptions or follow an inappropriate approximation…
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…
We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a…
We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
The second edition of the book "Roos, Stynes, Tobiska -- Robust Numerical Methods for Singularly Perturbed Differential Equations" appeared many years ago and was for many years a reliable guide into the world of numerical methods for…
We review recent progress in the study of infinite-dimensional stochastic differential equations with symmetry. This paper contains examples arising from random matrix theory.
This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like…