Related papers: Explicit formulae in probability and in statistica…
We show that the Politzer theorem on the equations of motion implies approximate constraints on the quark correlator, restricting considerably, for sufficiently large Q^2, the number of independent distribution functions that characterize…
When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary).…
We present an elementary method of explicit calculation of Young measures for certain class of functions. This class contains in particular functions of a highly oscillatory nature which appear in optimization problems and homogenization…
The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the…
This is an expository talk on a topic of classical analysis, arising from the VMO theory of the topological degree due to Br\'ezis and Nirenberg (1995). We sketch the history of the subject and some of its recent developments. The paper is…
In this paper, we review the construction and large $N$ study of the continuous two-dimensional Yang--Mills theory with gauge group $\mathrm{U}(N)$ through probability, combinatorics and representation theory. In the first part, we define…
Extending the work of Freese and Cook, which develop the basic theory of calculus and power series over real associative algebras, we examine what can be said about the logarithmic functions over an algebra. In particular, we find that for…
It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime…
The Maxwell integral equations expressing Ampere's and Faraday's laws are shown to be affected by heavy physical approximations. The usual deduction from them, moreover, of the corresponding set of differential Maxwell equations is based,…
The graphs induced by partition logics allow a dual probabilistic interpretation: a classical one for which probabilities lie on the convex hull of the dispersion-free weights, and another one, suggested independently from the quantum Born…
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…
This work is devoted to direct mass transportation proofs of families of functional inequalities in the context of one-dimensional free probability, avoiding random matrix approximation. The inequalities include the free form of the…
The article is devoted to the expansion of iterated Ito stochastic integrals of second multiplicity based on expansion of the Brownian motion (standard Wiener process) using complete orthonormal systems of functions in the space $L_2([t,…
The statistical methods used in deriving physics results in the BaBar collaboration are reviewed, with especial emphasis on areas where practice is not uniform in particle physics.
For a L\'evy process $\xi=(\xi_t)_{t\geq0}$ drifting to $-\infty$, we define the so-called exponential functional as follows \[{\rm{I}}_{\xi}=\int_0^{\infty}e^{\xi_t} dt.\] Under mild conditions on $\xi$, we show that the following…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…
We give asymptotic formulas for some average values of the Euler function on shifted smooth numbers. The result is based on various estimates on the distribution of smooth numbers in arithmetic progressions which are due to A. Granville and…
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
The concept of the elegant work introduced by Levai in Ref. [5] is extended for the solutions of the Schrodinger equation with more realistic other potentials used in different disciplines of physics. The connection between the present…