In the Idea of Limits video, we introduce the idea of limits and discuss how it underpins all of the major concepts in calculus. In the Limit Laws video, we introduce the limit laws and discuss how to ...

Random fields provide a versatile mathematical framework to describe spatially dependent phenomena, ranging from physical systems and quantum chaos to cosmology and spatial statistics. Underpinning ...

We study geometric moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under a Dini-continuity condition, a central limit theorem for ...

We derive limit theorems for the empirical distribution function of "devolatilized" increments of an Ito semimartingale observed at high frequencies. These "devolatilized" increments are formed by ...

Properties of the real numbers, infimum and supremum of sets. Numerical sequences and series. Limits of functions, continuous functions, intermediate value theorem, uniform continuity. Differentiation ...

Universality theorems occupy a central role in analytic number theory, demonstrating that families of analytic functions—including the prototypical Riemann zeta-function—can approximate an extensive ...