More Like this

1. The Gauss Image Problem

   https://doi.org/10.1002/cpa.21898  

   Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong; Zhao, Yiming (July 2020, Communications on Pure and Applied Mathematics)

   null (Ed.)
2. Exponential integrability in Gauss space

   https://doi.org/10.2140/apde.2023.16.1271  

   Ivanisvili, Paata; Russell, Ryan (January 2023, Analysis & PDE)
3. A Modern Gauss–Markov Theorem

   https://doi.org/10.3982/ECTA19255  

   Hansen, Bruce E. (January 2022, Econometrica)

   This paper presents finite‐sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss–Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares estimator, depending on the assumption on the error covariances. These results show that we can drop the label “linear estimator” from the pedagogy of the Gauss–Markov theorem. Instead of referring to these estimators as BLUE, they can legitimately be called BUE (best unbiased estimators). 

   more » « less
4. Higher Gauss sums of modular categories

   https://doi.org/10.1007/s00029-019-0499-2  

   Ng, Siu-Hung; Schopieray, Andrew; Wang, Yilong (October 2019, Selecta Mathematica)
5. Spontaneously interacting qubits from Gauss-Bonnet

   https://doi.org/10.1007/JHEP02(2024)007  

   Prudhoe, Sean; Kumar, Rishabh; Shandera, Sarah (February 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Building on previous constructions examining how a collection of small, locally interacting quantum systems might emerge via spontaneous symmetry breaking from a single-particle system of high dimension, we consider a larger family of geometric loss functionals and explicitly construct several classes of critical metrics which “know about qubits” (KAQ). The loss functional consists of the Ricci scalar with the addition of the Gauss-Bonnet term, which introduces an order parameter that allows for spontaneous symmetry breaking. The appeal of this method is two-fold: (i) the Ricci scalar has already been shown to have KAQ critical metrics and (ii) exact equations of motions are known for loss functionals with generic curvature terms up to two derivatives. We show that KAQ critical metrics, which are solutions to the equations of motion in the space of left-invariant metrics with fixed determinant, exist for loss functionals that include the Gauss-Bonnet term. We find that exploiting the subalgebra structure leads us to natural classes of KAQ metrics which contain the familiar distributions (GUE, GOE, GSE) for random Hamiltonians. We introduce tools for this analysis that will allow for straightfoward, although numerically intensive, extension to other loss functionals and higher-dimension systems. 

   more » « less