Related papers: Finite Free Entropy and Free Group Factors

In this letter, we give a concise, closed-form expression for the differential entropy of the sum of two independent, non-identically-distributed exponential random variables. The derivation is straightforward, but such a concise entropy…

A calculation of the one loop gravitational self-energy graph in non-anticommutative quantum gravity reveals that graviton loops are damped by internal momentum dependent factors in the modified propagator and the vertex functions. The…

We study the entropy production in non-equilibrium quantum systems without dissipation, which is generated exclusively by the spontaneous breaking of time-reversal invariance. Systems which preserve the total energy and particle number and…

We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…

We prove that finitary isomorphisms with finite expectation exist between Bernoulli shifts over the same free group only if the shifts have the same distribution. This generalizes the integer case result of Schmidt. We provide new proofs of…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively…

In this article we classify all $L_9$-free finite groups.

We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element centralisers are all soluble, and a reduction theorem for the…

We construct a finitely presented non-amenable group without free non-cyclic subgroups thus providing a finitely presented counterexample to von Neumann's problem. Our group is an extension of a group of finite exponent n >> 1 by a cyclic…

We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants and the bi-free…

For $G$ and $H_1,\dots, H_n$ finite groups, does there exist a $3$-manifold group with $G$ as a quotient but no $H_i$ as a quotient? We answer all such questions in terms of the group cohomology of finite groups. We prove non-existence with…

Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an…

We prove that entire transcendental holomorphic functions with an omitted value have infinite entropy. A proof for general transcendental entire functions will be given in an upcoming paper.

We prove that finitely generated virtually free groups are stable in permutations. As an application, we show that almost-periodic almost-automorphisms of labelled graphs are close to periodic automorphisms.

In this paper, we will construct the graph free product of noncommutative probability space. This is the attempt to explain and observe the combinatorial-object-depending probabilistic structure.

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all…

We prove that the orthogonal free quantum group factors $\mathcal{L}(\mathbb{F}O_N)$ are strongly $1$-bounded in the sense of Jung. In particular, they are not isomorphic to free group factors. This result is obtained by establishing a…

We prove a finiteness result for the systolic area of groups, answering a question of M. Gromov. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of~2-complexes whose systolic area is uniformly…

We prove the existence of manifolds with almost maximal volume entropy which are not hyperbolic.