Related papers: A Bilateral version of Shannon-Breiman-McMillan Th…

An extension of the Shannon-McMillan-Breiman theorem to a class of non-commutative dynamical systems is given.

The Shannon-McMillan-Breiman theorem is one of the most important results in information theory, which can describe the random ergodic process, and its proof uses the famous Birkhoff ergodic theorem, so it can be seen that it plays a…

We give a new proof of quantum Shannon-McMillan theorem, extending it to AF $C^*$-systems. Our proof is based on the variational principle, instead of the classical Shannon-McMillan theorem.

We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schr\"odinger--Poisson system.

We notice new Hermitian counterpart of Swanson's Hamiltonian.

We give an equivalent finitary reformulation of the classical Shannon-McMillan-Breiman theorem which has an immediate translation to the case of ergodic quantum lattice systems. This version of a quantum Breiman theorem can be derived from…

In this paper, we present a new form of the Hahn-Banach Theorem in terms of the sub-additive convex functions.

New version, including a variant of Quillen's proof of the Solomon-Tits theorem.

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.

We provide new Schmidt-type results through an investigation of two bijections, which are results involving partitions with parts counted only at given indices. Mork's bijection, the first of these, was originally given as a proof of…

We present a Cameron--Martin type quasi-invariance theorem for subordinate Brownian motion. As applications, we establish an integration by parts formula and construct a gradient operator on the path space of subordinate Brownian motion,…

In this paper we give a bijective proof for a relation between uni- bi- and tricellular maps of certain topological genus. While this relation can formally be obtained using Matrix-theory as a result of the Schwinger-Dyson equation, we here…

Given a II$_1$ factor M and a masa A of M, we prove a version of the Schur-Horn Theorem, together with a contractive version. These results are inspired on a recent conjecture of Arveson and Kadison (math.OA/0508482).

We show a new large sieve version of the Brun-Titchmarsh theorem.

We show how an approach to Smith Theory about group actions on CW-complexes using Bredon cohomology can be adapted to work for algebraic varieties.

We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.

We show that any finite group $G$ there exists a bijction $f$ from $G$ onto $C_{n}$ such that $o(x)$ divides $o(f(x))$ for all $x\in G$. This confirm Problem 18.1 in [7].

In this paper we show the renormalizability of the translation invariant noncommutative Chern-Simons theory, motivated by the work done on noncommutative scalar field theory [06]. We add a new term to the bilinear part of the action. In…

In this paper we use the power of the outer exponential $\Lambda^B$ of a bivector $B$ to see the so-called invariant decomposition from a different perspective. This is deeply connected with the eigenvalues for the adjoint action of $B$, a…

We propose a new refinement of the McKay conjecture and we prove it for symmetric groups.