相关论文: Growth estimates for discrete quantum groups
Consider a finite dimensional Lie algebra L with an action of a finite group G over a field of characteristic 0. We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of polynomial G-identities of L. As a…
Nekrashevych conjectured that the iterated monodromy groups of quadratic polynomials with preperiodic critical orbit have intermediate growth. We illustrate some of the difficulties that arise in attacking this conjecture and prove…
This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong…
Given a real semisimple connected Lie group $G$ and a discrete subgroup $\Gamma < G$ we prove a precise connection between growth rates of the group $\Gamma$, polyhedral bounds on the joint spectrum of the ring of invariant differential…
There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over $\mathbb{R}$ or $\mathbb{C}$, geometric statements on growth often have geometric proofs, what little is known over finite…
The main aim of this paper is to study the growth of solutions of higher order linear differential equations using the concepts of $(\alpha ,\beta ,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-type. We obtain some results which improve…
Gromov's theorem states that a finitely generated group has polynomial growth if and only if it is virtually nilpotent. A key ingredient in its proof is the small doubling property. In this work, we study entropy analogues of this property…
We show that the space of harmonic functions on a finitely generated infinite group G is finite dimensional if, and only if, G has a finite-index subgroup isomorphic to the integers. A key tool is Wilkie and van den Dries's quantitative…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
We have put forward a new unified framework which provides a consistent and rather complete account of the growth index of matter perturbations in the regime where the dark energy is allowed to have clustering. In particular, we find that…
We introduce the analog of Bohr compactification for discrete quantum groups on C*-algebra level. The cases of unimodular and general C*-algebraic discrete quantum groups are treated separately. The passage from the former case to the…
We study the growth of degrees in many autonomous and non-autonomous lattice equations defined by quad rules with corner boundary values, some of which are known to be integrable by other characterisations. Subject to an enabling…
We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.
We study the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semi-simple Lie group using an extension of the method due to Borel and Prasad.
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
Recently we have shown a structure theorem for locally compact groups of polynomial growth. We give now some applications on various growth functions and relations to FC-G - series. In addition, we show some results on related classes of…
We investigate the spectrum of 2-dimensional canonical systems in the limit circle case. It is discrete and, by the Krein-de Branges formula, cannot be more dense than the integers. But in many cases it will be more sparse. The spectrum of…
We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult.
In this paper, we deal with the growth and oscillation of solutions of higher order linear differential equations. Under the conditions that there exists a coefficient which dominates the other coefficients by its lower $% (\alpha ,\beta…