Related papers: Discrete Complex Analysis and Probability
Application of the intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few new discretizations of motion of the Euler top sharing…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
A certain representation for the Heisenberg algebra in finite-difference operators is established. The Lie-algebraic procedure of discretization of differential equations with isospectral property is proposed. Using $sl_2$-algebra based…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
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…
A class of discrete equations is considered from three perspectives corresponding to three measures of the complexity of solutions: the (hyper-) order of meromorphic solutions in the sense of Nevanlinna, the degree growth of iterates over a…
We investigate the high resolution coding problem for solutions of stochastic differential equations in the L^p[0,1]- and the C[0,1]-space. Tight asymptotic estimates are found under weak regularity assumptions. The main technical tool is a…
We discuss certain recent metric space methods and some of the possibilities these methods provide, with special focus on various generalizations of Lyapunov exponents originally appearing in the theory of dynamical systems and differential…
We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics,…
Parameter estimation in HEP experiments often involves Monte-Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
We consider options that pay the complexity deficiency of a sequence of up and down ticks of a stock upon exercise. We study the price of European and American versions of this option numerically for automatic complexity, and theoretically…
`Dual composition', a new method of constructing energy-preserving discretizations of conservative PDEs, is introduced. It extends the summation-by-parts approach to arbitrary differential operators and conserved quantities. Links to…
This paper introduces a general class of Replicator-Mutator equations on a multi-dimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fockker-Planck-Kolmogorov…
We solve the Dirichlet problem in the unit disc and derive the Poisson formula using very elementary methods and explore consequent simplifications in other foundational areas of complex analysis.