Related papers: An Introduction To Langer's Theory
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert…
In this article,a three parameter generalisation of inverse lindley distribution is obtained, with the purpose of obtaining a more flexible model relative to the behaviour of hazard rate functions. Various statistical properties such as…
These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical…
This paper combines the decomposition technique ($\sigma$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point…
This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and…
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged "statistical"…
We present a method to compute pairing fluctuations on top of the Gutzwiller approximation (GA). Our investigations are based on a charge-rotational invariant GA energy functional which is expanded up to second order in the pair…
The present study provides another look on Lamperti's theorem on recurrence or transience of stochastic sequences. We establish connection between Lamperti's theorem and the recent result by the author [V. M. Abramov, Theor. Probab. Math.…
In various contexts in mathematical physics one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the…
The dynamical likelihood method for analysis of high energy collider events is reformulated. The method is to reconstruct the elementary parton state from observed quantities. The basic assumption is that each of final state partons…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
Large deviation theory (LDT) provides a mathematical framework to quantify the probabilities of rare events in stochastic systems. In this study, we applied LDT to model a chemical reaction system and demonstrated that the fluctuation…
The concept of the Wigner function is used to construct a semi-classical kinetic theory describing the evolution of the axial-current phase-space density of spin-1/2 particles in the relaxation time approximation. The resulting approach can…
Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these forward models do not admit tractable densities forcing…
For a positive self-similar Markov process, X, we construct a local time for the random set, $\Theta$, of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of X out of its…
Contraction properties of the Riccati operator are studied within the context of non-stationary linear-quadratic optimal control. A lifting approach is used to obtain a bound on the rate of strict contraction, with respect to the Riemannian…
In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical schemes for the committor function, the central object of…
Quantum kinetic theory is an important tool for studying non-equilibrium, non-perturbative and non-linear interactions within an open quantum system, and as such is able to provide an unprecedented view on particle production in the…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
The Landauer formula allows us to describe theoretically the conductance in terms of the transmission function in a mesoscopic system. We propose a general method to evaluate the transmission function in the complex domain for systems…