46,672 research outputs found
Some statistics on permutations avoiding generalized patterns
In the last decade a huge amount of articles has been published studying
pattern avoidance on permutations. From the point of view of enumeration,
typically one tries to count permutations avoiding certain patterns according
to their lengths. Here we tackle the problem of refining this enumeration by
considering the statistics "first/last entry". We give complete results for
every generalized patterns of type or as well as for some cases
of permutations avoiding a pair of generalized patterns of the above types.Comment: 5 figure
Detection of spatial pattern through independence of thinned processes
Let N, N' and N'' be point processes such that N' is obtained from N by
homogeneous independent thinning and N''= N- N'. We give a new elementary proof
that N' and N'' are independent if and only if N is a Poisson point process. We
present some applications of this result to test if a homogeneous point process
is a Poisson point process.Comment: 11 pages, one figur
Harness processes and harmonic crystals
In the Hammersley harness processes the real-valued height at each site i in
Z^d is updated at rate 1 to an average of the neighboring heights plus a
centered random variable (the noise). We construct the process "a la Harris"
simultaneously for all times and boxes contained in Z^d. With this
representation we compute covariances and show L^2 and almost sure time and
space convergence of the process. In particular, the process started from the
flat configuration and viewed from the height at the origin converges to an
invariant measure. In dimension three and higher, the process itself converges
to an invariant measure in L^2 at speed t^{1-d/2} (this extends the convergence
established by Hsiao). When the noise is Gaussian the limiting measures are
Gaussian fields (harmonic crystals) and are also reversible for the process.Comment: 21 pages. Revised version with minor changes. Version almost
identical to the one to be published in SP
Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
In [arXiv:0804.3035] we studied an interacting particle system which can be
also interpreted as a stochastic growth model. This model belongs to the
anisotropic KPZ class in 2+1 dimensions. In this paper we present the results
that are relevant from the perspective of stochastic growth models, in
particular: (a) the surface fluctuations are asymptotically Gaussian on a
sqrt(ln(t)) scale and (b) the correlation structure of the surface is
asymptotically given by the massless field.Comment: 13 pages, 4 figure
Supersymmetric non-Abelian noncommutative Chern-Simons theory
In this work, we study the three-dimensional non-Abelian noncommutative
supersymmetric Chern-Simons model with the U(N) gauge group. Using a superfield
formulation, we prove that, for the pure gauge theory, the Green functions are
one-loop finite in any gauge, if the gauge superpotential belongs to the
fundamental representation of ; this result also holds when matter in the
fundamental representation is included. However, the cancellation of both
ultraviolet and ultraviolet/infrared infrared divergences only happens in a
special gauge if the coupling of the matter is in the adjoint representation.
We also look into the finite one-loop quantum corrections to the effective
action: in the pure gauge sector the Maxwell together with its corresponding
gauge fixing action are generated; in the matter sector, the Chern-Simons term
is generated, inducing a shift in the classical Chern-Simons coefficient.Comment: 16 pages, 3 figures, revtex4, enhanced discussion, mainly of the
finite part of quantum corrections, and the shift in the Chern-Simons
coefficien
Complete electroweak one loop contributions to the pair production cross section of MSSM charged and neutral Higgs bosons in e+e- collisions
In this paper, we review the production cross section for charged and neutral
Higgs bosons pairs in collisions beyond the tree level, in the
framework of the Minimal Supersymmetric Standard Model (MSSM). A complete list
of formulas for all electroweak contributions at the one loop level is given. A
numerical code has been developed in order to compute them accurately and, in
turn, to compare the MSSM Higgs bosons pair production cross sections at tree
level and at the one loop level.Comment: 58 pages, 3 eps figure
Matrix Models, Argyres-Douglas singularities and double scaling limits
We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level
superpotential whose matrix model spectral curve develops an A_{n+1}
Argyres-Douglas singularity. We evaluate the coupling constants of the
low-energy U(1)^n theory and show that the large N expansion is singular at the
Argyres-Douglas points. Nevertheless, it is possible to define appropriate
double scaling limits which are conjectured to yield four dimensional
non-critical string theories as proposed by Ferrari. In the Argyres-Douglas
limit the n-cut spectral curve degenerates into a solution with n/2 cuts for
even n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been
corrected and the calculation of the coupling constants of the low-energy
theory has been adde
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