Non-Archimedean statistical field theory

Non-Archimedean Ergodic Theory and Pseudorandom Generators

The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions (arithmetic and bitwise logical ones) as continuous functions on the space of 2-adic integers. Within this approach, a PRNG is considered as a dynamical system and is...

Direct Images in Non-archimedean Arakelov Theory

In this paper we develop a formalism of direct images for metrized vector bundles in the context of the non-archimedean Arakelov theory introduced in our joint work [BGS] with S. Bloch, and we prove a Riemann-Roch-Grothendieck theorem for this direct image. The new ingredient in the construction of the direct image is a non archimedean " analytic torsion current ". Let K be the fraction field o...

The Non-Archimedean Theory of Discrete Systems

In the paper, we study behaviour of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behaviour of the system w.r.t. variety of word transformations performed by the system: We call a system completely transitive if, given arbitrary pair a, b of finite words that have equal lengths, the system A, while evolution during (discrete...

Non-archimedean Nevanlinna Theory in Several Variables and the Non-archimedean Nevanlinna Inverse Problem

Cartan’s method is used to prove a several variable, non-Archimedean, Nevanlinna Second Main Theorem for hyperplanes in projective space. The corresponding defect relation is derived, but unlike in the complex case, we show that there can only be finitely many non-zero non-Archimedean defects. We then address the non-Archimedean Nevanlinna inverse problem, by showing that given a set of defects...

Kirillov Theory for Gl2( ) Where Is a Division Algebra over a Non-archimedean Local Field