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The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is…
We derive an efficient method to calculate exceedance probabilities (EP) for the Dirichlet distribution when the number of event types is larger than two. Also, we present an intuitive application of Dirichlet EPs and compare our method to…
It is shown that in the two-exponential version of Liouville theory the coefficients of the three-point functions of vertex operators can be determined uniquely using the translational invariance of the path integral measure and the…
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
We give an account of the arguments that lead from the assumption of the existence of exceptional characters to the asymptotics in related ranges for the counting function of twin primes.
The paper deals with different properties of polynomials in random elements: bounds for characteristics functionals of polynomials, stochastic generalization of the Vinogradov mean value theorem, characterization problem, bounds for…
This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility,…
An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their…
A natural problem in the context of the coupon collector's problem is the behavior of the maximum of independent geometrically distributed random variables (with distinct parameters). This question has been addressed by Brennan et al.…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
A bi-univalent function is a univalent function defined on the unit disk with its inverse also univalent on the unit disk. Estimates for the initial coefficients are obtained for bi-univalent functions belonging to certain classes defined…
This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…
Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional…
The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study…
We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…
Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.