7 research outputs found
From interacting particle systems to random matrices
In this contribution we consider stochastic growth models in the
Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large
time distribution and processes and their dependence on the class on initial
condition. This means that the scaling exponents do not uniquely determine the
large time surface statistics, but one has to further divide into subclasses.
Some of the fluctuation laws were first discovered in random matrix models.
Moreover, the limit process for curved limit shape turned out to show up in a
dynamical version of hermitian random matrices, but this analogy does not
extend to the case of symmetric matrices. Therefore the connections between
growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor
corrections in scaling of section 2.
On the partial connection between random matrices and interacting particle systems
In the last decade there has been increasing interest in the fields of random
matrices, interacting particle systems, stochastic growth models, and the
connections between these areas. For instance, several objects appearing in the
limit of large matrices arise also in the long time limit for interacting
particles and growth models. Examples of these are the famous Tracy-Widom
distribution functions and the Airy_2 process. The link is however sometimes
fragile. For example, the connection between the eigenvalues in the Gaussian
Orthogonal Ensembles (GOE) and growth on a flat substrate is restricted to
one-point distribution, and the connection breaks down if we consider the joint
distributions. In this paper we first discuss known relations between random
matrices and the asymmetric exclusion process (and a 2+1 dimensional
extension). Then, we show that the correlation functions of the eigenvalues of
the matrix minors for beta=2 Dyson's Brownian motion have, when restricted to
increasing times and decreasing matrix dimensions, the same correlation kernel
as in the 2+1 dimensional interacting particle system under diffusion scaling
limit. Finally, we analyze the analogous question for a diffusion on (complex)
sample covariance matrices.Comment: 31 pages, LaTeX; Added a section concerning the Markov property on
space-like path
Measurement of CP violation parameters and polarisation fractions in decays
The first measurement of asymmetries in the decay and an updated measurement of its branching
fraction and polarisation fractions are presented. The results are obtained
using data corresponding to an integrated luminosity of of
proton-proton collisions recorded with the LHCb detector at centre-of-mass
energies of and . Together with constraints from , the results are used to constrain additional contributions due
to penguin diagrams in the -violating phase , measured
through decays to charmonium.Comment: 39 pages, 7 tables, 8 figures. All figures and tables, along with any
supplementary material and additional information, are available at
https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-034.htm
Conservation status of the American horseshoe crab, (Limulus polyphemus): a regional assessment
Molecular differences between arterial and venous grafts in the first year after coronary artery bypass grafting
Cutaneous Adnexal Tumors
The main subtypes of cutaneous adnexal tumors aredescribed in this chapter in accordance with the latestclassification of this complex and heterogeneous groupof disorder