98 research outputs found
Fully packed loop configurations : polynomiality and nested arches
International audienceThis extended abstract proves that the number of fully packed loop configurations whose link pattern consists of two noncrossing matchings separated by m nested arches is a polynomial in m. This was conjectured by Zuber (2004) and for large values of m proved by Caselli et al. (2004
The relation between alternating sign matrices and descending plane partitions: pairs of equivalent statistics
There is the same number of alternating sign matrices (ASMs) as
there is of descending plane partitions (DPPs) with parts no greater than ,
but finding an explicit bijection is an open problem for about years now.
So far, quadruples of statistics on ASMs and on DPPs that have the same joint
distribution have been identified. We introduce extensions of ASMs and of DPPs
along with statistics on each extension, and show that the two families
of statistics have the same joint distribution. The ASM-DPP equinumerosity is
obtained as an easy consequence by considering the -enumerations of these
extended objects with respect to one pair of the pairs of statistics. One
may speculate that the fact that these extensions might be necessary to have
this significance increase in the number of statistics, as well as the
involvement of signs when specializing to ASMs and DPPs may hint at the
obstacles in finding an explicit bijection between ASMs and DPPs. One important
tool for our proof is a multivariate generalization of the operator formula for
the number of monotone triangles with prescribed bottom row that generalizes
Schur functions
Fully packed loop configurations : polynomiality and nested arches
This extended abstract proves that the number of fully packed loop configurations whose link pattern consists of two noncrossing matchings separated by m nested arches is a polynomial in m. This was conjectured by Zuber (2004) and for large values of m proved by Caselli et al. (2004
Shot noise in the chaotic-to-regular crossover regime
We investigate the shot noise for phase-coherent quantum transport in the
chaotic-to-regular crossover regime. Employing the Modular Recursive Green's
Function Method for both ballistic and disordered two-dimensional cavities we
find the Fano factor and the transmission eigenvalue distribution for regular
systems to be surprisingly similar to those for chaotic systems. We argue that
in the case of regular dynamics in the cavity, diffraction at the lead openings
is the dominant source of shot noise. We also explore the onset of the
crossover from quantum to classical transport and develop a quasi-classical
transport model for shot noise suppression which agrees with the numerical
quantum data.Comment: 4 pages, 3 figures, submitted to Phys.Rev.Let
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