Related papers: Character theory approach to Sato-Tate groups
Let $A$ be an abelian variety defined over a number field and let $G$ denote its Sato-Tate group. Under the assumption of certain standard conjectures on $L$-functions attached to the irreducible representations of $G$, we study the…
We investigate the description of statistical field theories using Daubechies' orthonormal compact wavelets on a lattice. A simple variational approach is used to extend mean field theory and make predictions for the fluctuation strengths…
A compact Lie group G and a faithful complex representation V determine a Sato-Tate measure, defined as the direct image of Haar measure on G with respect to the character of V. We give a necessary and sufficient condition for a Sato-Tate…
We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.
This paper focuses on a stochastic formulation of Bayesian attitude estimation on the special orthogonal group. In particular, an exponential probability density model for random matrices, referred to as the matrix Fisher distribution is…
Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the…
Let $G$ be a group and $\alpha: G \times G \to G$ denote the commutator map. In the case of finite groups, Frobenius gave the formula to compute the cardinalities of the fibres $\alpha^{-1}(g)$ in terms of the character values $\chi(g)$ for…
Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the…
We consider the curves $y^2=x^{2^m} -1$ and $y^2=x^{2^{d}+1}-x$ over the rationals. These curves are related via their associated Jacobian varieties in that the Jacobians of the latter appear as factors of the Jacobians of the former. One…
We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let $G$ be a reductive group over a number field $F$ which admits discrete series representations at…
We determine the Sato-Tate groups and prove the generalized Sato-Tate conjecture for the Jacobians of curves of the form $$ y^2=x^p-1 \text{ and } y^2=x^{2p}-1,$$ where $p$ is an odd prime. Our results rely on the fact the Jacobians of…
The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between…
Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…
With suitable order of limits, as p, m, and n all tend to infinity, the distribution of the normalized trace of Frobenius on H^1 of a "random" plane curve of degree n over the field with p^m elements, tends to a Gaussian distribution. The…
Resultate der Charaktertheorie der symmetrischen Gruppe werden verwendet, um eine Verteilungsfunktion f\"ur das Geschlecht zuf\"allig gew\"ahlter Origamis zu erhalten. -- Results from the character theory of the symmetric group are used to…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
Motivated by analogous results for the symmetric group and compact Lie groups, we study the distribution of the number of fixed vectors of a random element of a finite classical group. We determine the limiting moments of these…
Associated to an abelian variety over a number field are several interesting and related groups: the motivic Galois group, the Mumford-Tate group, $\ell$-adic monodromy groups, and the Sato-Tate group. Assuming the Mumford-Tate conjecture,…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
Research on social contagion dynamics has not yet including a theoretical analysis of the ubiquitous local trend imitation (LTI) characteristic. We propose a social contagion model with a tent-like adoption probability distribution to…