Large deviations and a new sum rule for spectral matrix measures of the Jacobi ensemble

2019 ◽  
Vol 10 (01) ◽  
pp. 2150008 ◽  
Author(s):  
Fabrice Gamboa ◽  
Jan Nagel ◽  
Alain Rouault
Keyword(s):  
Large Deviations ◽  
Matrix Theory ◽  
Sum Rules ◽  
Large Deviation ◽  
Intermediate Step ◽  
Spectral Matrix ◽  
Sum Rule ◽  
Jacobi Ensemble ◽  
Reference Measure ◽  
Matrix Measures

We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509–559] for spectral measures of classical ensembles (Gauss–Hermite, Laguerre, Jacobi) and it was extended to spectral matrix measures of the Hermite and Laguerre ensemble in [Sum rules and large deviations for spectral matrix measures, Bernoulli 25(1) (2018) 712–741]. In this paper, we consider the remaining case of spectral matrix measures of the Jacobi ensemble. Our main results are a large deviation principle for such measures and a sum rule for matrix measures with reference measure the Kesten–McKay law. As an important intermediate step, we derive the distribution of matricial canonical moments of the Jacobi ensemble.

scholarly journals Sum rules and large deviations for spectral measures on the unit circle

2017 ◽  
Vol 06 (01) ◽  
pp. 1750005
Author(s):  
Fabrice Gamboa ◽  
Jan Nagel ◽  
Alain Rouault
Keyword(s):  
Large Deviations ◽  
Unit Circle ◽  
Matrix Theory ◽  
Sum Rules ◽  
Large Deviation ◽  
Equilibrium Measure ◽  
Spectral Matrix ◽  
Sum Rule ◽  
Funct Anal ◽  
Matrix Measures

This work is a companion paper of [F. Gamboa, J. Nagel and A. Rouault, Sum rules via large deviations, J. Funct. Anal. 270 (2016) 509–559] and [F. Gamboa, J. Nagel and A. Rouault, Sum rules and large deviations for spectral matrix measures, preprint (2016), arXiv:1601.08135 ] (see also [J. Breuer, B. Simon and O. Zeitouni, Large deviations and sum rules for spectral theory — A pedagogical approach, to appear in J. Spectr. Theory, preprint (2016), arXiv:1608.01467 ]). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned essentially with measures on the unit circle whose support is an arc that is possibly proper. We particularly focus on two-matrix models. The first one is the Gross–Witten (GW) ensemble. In the gapped regime, we give a probabilistic interpretation of a Simon sum rule. The second matrix model is the Hua–Pickrell (HP) ensemble. Unlike the GW ensemble the potential is here infinite at one point. Surprisingly, but as in [F. Gamboa, J. Nagel and A. Rouault, Sum rules via large deviations, J. Funct. Anal. 270 (2016) 509–559], we obtain a completely new sum rule for the deviation to the equilibrium measure of the HP ensemble. The case of spectral matrix measures is also studied. Indeed, in the case of HP ensemble, we extend our earlier works on large deviation for spectral matrix measure [F. Gamboa, J. Nagel and A. Rouault, Sum rules and large deviations for spectral matrix measures, preprint (2016), arXiv:1601.08135 ] and get here also a completely new sum rule.

scholarly journals Sum rules and large deviations for spectral matrix measures

Bernoulli ◽  
2019 ◽  
Vol 25 (1) ◽  
pp. 712-741 ◽  
Author(s):  
Fabrice Gamboa ◽  
Jan Nagel ◽  
Alain Rouault
Keyword(s):  
Large Deviations ◽  
Sum Rules ◽  
Spectral Matrix ◽  
Matrix Measures

scholarly journals Large deviations and sum rules for spectral theory. A pedagogical approach

2018 ◽  
Vol 8 (4) ◽  
pp. 1551-1581 ◽  
Author(s):  
Jonathan Breuer ◽  
Barry Simon ◽  
Ofer Zeitouni
Keyword(s):  
Large Deviations ◽  
Spectral Theory ◽  
Sum Rules ◽  
Pedagogical Approach

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

scholarly journals L-edge sum rule analysis on 3d transition metal sites: from d10to d0and towards application to extremely dilute metallo-enzymes

2018 ◽  
Vol 20 (12) ◽  
pp. 8166-8176 ◽  
Author(s):  
Hongxin Wang ◽  
Stephan Friedrich ◽  
Lei Li ◽  
Ziliang Mao ◽  
Pinghua Ge ◽  
...  
Keyword(s):  
Absorption Spectrum ◽  
Transition Metal ◽  
Metal Complex ◽  
Sum Rules ◽  
Sum Rule ◽  
X Ray ◽  
Metal Site ◽  
Integrated Intensity ◽  
Rule Analysis ◽  
X Ray Absorption

According to L-edge sum rules, the number of 3d vacancies at a transition metal site is directly proportional to the integrated intensity of the L-edge X-ray absorption spectrum (XAS) for the corresponding metal complex.

COMMENTS ON QCD SUM-RULE CALCULATIONS OF EXCLUSIVE TWO-BODY DECAYS OF CHARMED MESONS

1989 ◽  
Vol 04 (09) ◽  
pp. 877-883 ◽  
Author(s):  
LING-LIE CHAU ◽  
HAI-YANG CHENG
Keyword(s):  
Experimental Data ◽  
Sum Rules ◽  
Theoretical Calculations ◽  
Charmed Mesons ◽  
Qcd Sum Rules ◽  
Generic Structure ◽  
Sum Rule ◽  
Quark Diagram ◽  
Model Independent ◽  
Decays Of Charmed Mesons

Exclusive two-body decay amplitudes of charmed mesons evaluated by Blok and Shifman (BS) using QCD sum rules are analyzed using the model-independent quark-diagram scheme, which helps to pin point the generic structure of the BS calculations, and their difficulties when compared with the experimental data. We also point out what experimental improvements on the data and which new data are most helpful in sharpening these comparisons. Some comments on possible ways of further improving the theoretical calculations are given.

scholarly journals LARGE DEVIATIONS FOR FLOWS OF INTERACTING BROWNIAN MOTIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 315-339 ◽  
Author(s):  
A. A. DOROGOVTSEV ◽  
O. V. OSTAPENKO
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Flows ◽  
Brownian Motions ◽  
Deviation Principle ◽  
And Brownian Motion

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment.

scholarly journals REVIEW ON QCD SUM RULES CALCULATIONS FOR EXOTICS CHARMONIUM

2011 ◽  
Vol 02 ◽  
pp. 36-40
Author(s):  
MARINA NIELSEN
Keyword(s):  
Sum Rules ◽  
Mass Region ◽  
Qcd Sum Rules ◽  
Sum Rule ◽  
Rule Approach ◽  
New States

Many new states in the charmonium mass region were recently discovered by the BaBar, Belle and CDF Collaborations. We use the QCD Sum Rule approach to study the possible structure of some of these states.

Large deviations in the supercritical branching process

1993 ◽  
Vol 25 (04) ◽  
pp. 757-772 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Distribution Function ◽  
Large Deviations ◽  
Population Size ◽  
Branching Process ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Large Deviation Theory ◽  
Tail Behaviour ◽  
The Moment ◽  
Deviation Theory

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.

scholarly journals STATUS OF THE HADRONIC τ DETERMINATION OF Vus

2008 ◽  
Vol 23 (21) ◽  
pp. 3191-3195 ◽  
Author(s):  
K. MALTMAN ◽  
C. E. WOLFE ◽  
S. BANERJEE ◽  
M. RONEY ◽  
I. NUGENT
Keyword(s):  
Sum Rules ◽  
Branching Fractions ◽  
Sum Rule ◽  
Slow Convergence ◽  
Decay Data ◽  
Decay Modes ◽  
Good Agreement

We update the extraction of Vus from hadronic τ decay data in light of recent BaBar and Belle results on the branching fractions of a number of important strange decay modes. A range of sum rule analyses is employed, particular attention being paid to those based on “non-spectral weights”, developed previously to bring the slow convergence of the relevant integrated D = 2 OPE series under improved control. Results from the various sum rules are in good agreement with one another, but ~ 3σ below expectations based on 3-family unitarity.

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