Related papers: Random Kleinian Groups I: Random Fuchsian Groups
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution…
Measuring the effect of peers on individuals' outcomes is a challenging problem, in part because individuals often select peers who are similar in both observable and unobservable ways. Group formation experiments avoid this problem by…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
In number theory, great efforts have been undertaken to study the Cohen-Lenstra probability measure on the set of all finite abelian $p$-groups. On the other hand, group theorists have studied a probability measure on the set of all…
We describe a probability distribution on isomorphism classes of principally quasi-polarized p-divisible groups over a finite field k of characteristic p which can reasonably be thought of as "uniform distribution," and we compute the…
Random orthogonal matrices play an important role in probability and statistics, arising in multivariate analysis, directional statistics, and models of physical systems, among other areas. Calculations involving random orthogonal matrices…
We consider a discrete-time random motion, Markov chain on the Poincar\'{e} disk. In the basic variant of the model a particle moves along certain circular arcs within the disk, its location is determined by a composition of random…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…
Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of…
We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group.…
We consider models of random groups in which the typical group is of intermediate rank (in particular, it is not hyperbolic). These models are parallel to M. Gromov's well-known constructions and include for example a "density model" for…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
The main aim of the present set of notes is to give new, short and essentially self-contained proofs of some classical, as well as more recent, results about random walks on groups. For instance, we shall see that the drift characterization…
The Poisson and Martin boundaries for invariant random walks on the dual of the orthogonal quantum groups A_o(F), are identified with higher dimensional Podles spheres that we describe in terms of generators and relations. This provides the…
In this work, we will introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random groups under an additional dimension condition on the volume of…