42,746 research outputs found
Measurement of the dipole in the cross-correlation function of galaxies
It is usually assumed that in the linear regime the two-point correlation
function of galaxies contains only a monopole, quadrupole and hexadecapole.
Looking at cross-correlations between different populations of galaxies, this
turns out not to be the case. In particular, the cross-correlations between a
bright and a faint population of galaxies contain also a dipole. In this paper
we present the first attempt to measure this dipole. We discuss the four types
of effects that contribute to the dipole: relativistic distortions, evolution
effect, wide-angle effect and large-angle effect. We show that the first three
contributions are intrinsic anti-symmetric contributions that do not depend on
the choice of angle used to measure the dipole. On the other hand the
large-angle effect appears only if the angle chosen to extract the dipole
breaks the symmetry of the problem. We show that the relativistic distortions,
the evolution effect and the wide-angle effect are too small to be detected in
the LOWz and CMASS sample of the BOSS survey. On the other hand with a specific
combination of angles we are able to measure the large-angle effect with high
significance. We emphasise that this large-angle dipole does not contain new
physical information, since it is just a geometrical combination of the
monopole and the quadrupole. However this measurement, which is in excellent
agreement with theoretical predictions, validates our method for extracting the
dipole from the two-point correlation function and it opens the way to the
detection of relativistic effects in future surveys like e.g. DESI.Comment: 15 pages, 17 figures. v2: 20 pages, 17 figures. Section IIIc partly
rewritten, new section IIId, new figures 16 and 17. Main results unchanged.
Matches published version in JCA
Odd-flavored QCD_3 and Random Matrix Theory
We consider QCD_3 with an odd number of flavors in the mesoscopic scaling
region where the field theory finite-volume partition function is equivalent to
a random matrix theory partition function. We argue that the theory is parity
invariant at the classical level if an odd number of masses are zero. By
introducing so-called pseudo-orthogonal polynomials we are able to relate the
kernel to the kernel of the chiral unitary ensemble in the sector of
topological charge . We prove universality and are able to write the
kernel in the microscopic limit in terms of field theory finite-volume
partition functions.Comment: 12 pages, Latex2e, 1 figure. Misprints corrected, minor changes in
wording, one reference change
Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
We prove that general correlation functions of both ratios and products of
characteristic polynomials of Hermitian random matrices are governed by
integrable kernels of three different types: a) those constructed from
orthogonal polynomials; b) constructed from Cauchy transforms of the same
orthogonal polynomials and finally c) those constructed from both orthogonal
polynomials and their Cauchy transforms. These kernels are related with the
Riemann-Hilbert problem for orthogonal polynomials. For the correlation
functions we obtain exact expressions in the form of determinants of these
kernels. Derived representations enable us to study asymptotics of correlation
functions of characteristic polynomials via Deift-Zhou
steepest-descent/stationary phase method for Riemann-Hilbert problems, and in
particular to find negative moments of characteristic polynomials. This reveals
the universal parts of the correlation functions and moments of characteristic
polynomials for arbitrary invariant ensemble of symmetry class.Comment: 34page
Random matrices and the replica method
Recent developments [Kamenev and Mezard, cond-mat/9901110, cond-mat/9903001;
Yurkevich and Lerner, cond-mat/9903025; Zirnbauer, cond-mat/9903338] have
revived a discussion about applicability of the replica approach to description
of spectral fluctuations in the context of random matrix theory and beyond. The
present paper, concentrating on invariant non-Gaussian random matrix ensembles
with orthogonal, unitary and symplectic symmetries, aims to demonstrate that
both the bosonic and the fermionic replicas are capable of reproducing
nonperturbative fluctuation formulas for spectral correlation functions in
entire energy scale, including the self-correlation of energy levels, provided
no sigma-model mapping is used.Comment: 12 pages (latex), presentation clarified, misprints fixe
Random matrices, log-gases and Holder regularity
The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue
statistics of large real and complex Hermitian matrices with independent,
identically distributed entries are universal in a sense that they depend only
on the symmetry class of the matrix and otherwise are independent of the
details of the distribution. We present the recent solution to this
half-century old conjecture. We explain how stochastic tools, such as the Dyson
Brownian motion, and PDE ideas, such as De Giorgi-Nash-Moser regularity theory,
were combined in the solution.
We also show related results for log-gases that represent a universal model
for strongly correlated systems. Finally, in the spirit of Wigner's original
vision, we discuss the extensions of these universality results to more
realistic physical systems such as random band matrices.Comment: Proceedings of ICM 201
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