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Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…
In this paper a Monte-Carlo method for simulating the motion of fluid flow moving along a solid wall is proposed. The random vortex method in the present paper is established by using the reflection technology and perturbation technique.…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
The history of the development of Monte Carlo methods to solve the many-body problem in quantum mechanics is presented. The survey starts with the early attempts with the first available computers just after the war and extends until the…
This article is devoted to methods of construction and study of stochastic models based on Monte Carlo method. A model of Brownian motion, the construction and processing which brings to a world of random numbers and mathematical…
We discuss Brownian Motion from a more elementary viewpoint presented by Einstein in 1908. Later developments and applications are briefly reviewed.
Accelerator beam commissioning is a challenging and exciting period. It is generally the first integrated operation of the many systems in an accelerator and, most importantly, of the beam. First, general preparation is discussed. Then…
The article is a tribute to Hermann Minkowski leading from his geometry of numbers to an attempt at using Finsler geometry for a break of Lorentz invariance.
Stochastic methods for minimizing a convex integral functional, as initiated by Robbins and Monro in the early 1950s, rely on the evaluation of a gradient (or subgradient if the function is not smooth) and moving in the corresponding…
We suggest there is a need for a fresh perspective on the design and development of workflow systems and argue for a building blocks approach. We outline a description of this approach and define the properties of software building blocks.…
We prove the existence of recurrent initial configurations for the rotor walk on many graphs, including Z^d, and planar graphs with locally finite embeddings. We also prove that recurrence and transience of rotor walks are invariant under…
Path transformations are fundamental to the study of Brownian motion and related stochastic processes, offering elegant constructions of the Brownian bridge, meander, and excursion. Central to this theory is the well-established link…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
This paper contains my recollection of the creation and development of the so-called BFKL approach and my ideas about the ways of its further development.
This monograph provides a rigorous overview of theoretical and methodological aspects of probabilistic inference and learning with Stein's method. Recipes are provided for constructing Stein discrepancies from Stein operators and Stein…
In 1963-71, a group of people, myself included, formulated and perfected a new approach to physics problems, which eventually came to be known under the names of scaling, universality, and renormalization. This work formed the basis of a…
This paper explores how far the scientific discovery process can be automated. Using the identification of causally significant flow structures in two-dimensional turbulence as an example, it probes how far the usual procedure of planning…