Functional Analysis and Its Applications最新文献

We discuss the qualitatively new properties of random walks on groups that arise in the situation when the entropy of the step distribution is infinite.

Let (G) be a countable ergodic group of automorphisms of a measure space ((X,mu)) and (mathcal{N}[G]) be the normalizer of its full group ([G]). Problem: for a pair of measurable partitions (xi) and (eta) of the space (X), when does there exist an element (ginmathcal{N}[G]) such that (gxi=eta)? For a wide class of measurable partitions, we give a solution to this problem in the case where (G) is an approximately finite group with finite invariant measure. As a consequence, we obtain results concerning the conjugacy of the commutative subalgebras that correspond to (xi) and (eta) in the type (mathrm{II}_1) factor constructed via the orbit partition of the group (G).

For partially ordered sets ((X, preccurlyeq)), we consider the square matrices (M^{X}) with rows and columns indexed by linear extensions of the partial order on (X). Each entry ((M^{X})_{PQ}) is a formal variable defined by a pedestal of the linear order (Q) with respect to linear order (P). We show that all eigenvalues of any such matrix (M^{X}) are (mathbb{Z})-linear combinations of those variables.

The flows generated by the iterative dynamics of triangle reflections are analyzed. These flows are interpreted as the adiabatic dynamics of probe particles within the fundamental domain of the modular group. Two specific cases of lattices are considered: (a) those generated by reflections of equilateral triangles, and (b) those generated by reflections of rectangular isosceles triangles. We demonstrate that the stationary points of the flows for equilateral and isosceles triangles correspond to the “Golden” and the “Silver” ratios, respectively.

We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and the uniform measure, a (U(1)) case of (mathcal{N}=2^{*}) gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric “arcsin” law of Vershik–Kerov and Logan–Schepp.

The paper is devoted to the study of duality in the linear Kantorovich problem with a fixed barycenter. It is proved that Kantorovich duality holds for general lower semicontinuous cost functions on completely regular spaces. In the course of considering this subject, the question of representation of a continuous linear functional by a Radon measure is raised and solved, provided that the barycenter of the functional is given by a Radon measure. In addition, we consider two new barycentric optimization problems and prove duality results for them.

We define a Grothendieck ring of pairs of complex quasi-projective varieties (consisting of a variety and a subvariety). We describe (lambda)-structures on this ring and a power structure over it. We show that the conjectual symmetric power of the projective line with several orbifold points described by A. Fonarev is consistent with the symmetric power of this line with the set of distinguished points as a pair of varieties.

We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions (up to null-sets) for such actions.

The article studies bundle towers (M^{n+1}to M^{n}to dots to S^1), (geqslant 1), with fiber (S^1), where (M^n = L^n!/Gamma^n) are compact smooth nilmanifolds and (L^nthickapprox mathbb{R}^n) is a group of polynomial transformations of the line (mathbb{R}^1). The focus is on the well-known problem of calculating cohomology rings with rational coefficients of manifolds (M^n). Using the canonical bigradation in the de Rham complex of manifolds (M^n), we introduce the concept of polynomial Eulerian characteristic and calculate it for these manifolds.