arXiv subjects

Thomas Breuer

Publications and source records attributed to Thomas Breuer.

24 records · Page 2Linked to original sources

arXiv2013

Measuring Model Risk

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy, a Bregman distance, or an $f$-divergence. We give formulas for the calculation of distribution model risk and explicitly determine the worst case distribution from the set of plausible distributions. We also give formulas for the evaluation of divergence preferences describing ambiguity averse decision makers.

q-fin.RM↗

arXiv2012

GAP Computations Concerning Probabilistic Generation of Finite Simple Groups

This is a collection of examples showing how the GAP system can be used to compute information about the probabilistic generation of finite almost simple groups. It includes all examples that were needed for the computational results in the paper "Probabilistic generation of finite simple groups, II" by Thomas Breuer, Robert M. Guralnick, and William M. Kantor. The purpose of this writeup is twofold. On the one hand, the computations are documented this way. On the other hand, the GAP code shown for the examples can be used as test input for automatic checking of the data and the functions used.

math.RT↗

arXiv2012

GAP Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups

This is a collection of examples showing how the GAP system can be used to compute information about the generating graphs of finite groups. It includes all examples that were needed for the computational results in the paper "Hamiltonian cycles in the generating graphs of finite groups" by Thomas Breuer, Robert M. Guralnick, Andrea Lucchini, Attila Maróti, and Gábor P. Nagy. The purpose of this writeup is twofold. On the one hand, the computations are documented this way. On the other hand, the GAP code shown for the examples can be used as test input for automatic checking of the data and the functions used.

math.RT↗

arXiv2012

GAP computations needed in the proof of [DNT, Theorem 6.1 (ii)]

This is a collection of example computations that are cited in the Appendix of [DNT]. In each case, the aim is to show that the extension of a given finite simple group by an elementary abelian group of given rank has the property that not all complex irreducible characters of the same degree are Galois conjugate.

math.RT↗

arXiv2002

Kochen-Specker Theorem for Finite Precision Spin One Measurements

Unsharp spin 1 observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.

quant-ph↗

arXiv2002

A Kochen-Specker Theorem for Unsharp Spin 1 Observables

Unsharp spin observables are shown to arise from the fact that a residual uncertainty about the actual alignment of the measurement device remains. If the uncertainty is below a certain level, and if the distribution misalignments is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.

quant-ph↗