19,691 research outputs found
Local convergence of critical random trees and continuous-state branching processes
We study the local convergence of critical Galton-Watson trees and Levy trees
under various conditionings. Assuming a very general monotonicity property on
the functional of random trees, we show that random trees conditioned to have
large functional values always converge locally to immortal trees. We also
derive a very general ratio limit property for functionals of random trees
satisfying the monotonicity property. Then we move on to study the local
convergence of critical continuous-state branching processes, and prove a
similar result. Finally we give a definition of continuum condensation trees,
which should be the correct local limits for certain subcritical Levy trees
under suitable conditionings.Comment: 22 page
Frobenius splitting of projective toric bundles
We give several mild conditions on a toric bundle on a nonsingular toric
variety under which the projectivization of the toric bundle is Frobenius
split.Comment: 9 pages. Comments are welcom
Optimal Monotone Drawings of Trees
A monotone drawing of a graph G is a straight-line drawing of G such that,
for every pair of vertices u,w in G, there exists abpath P_{uw} in G that is
monotone in some direction l_{uw}. (Namely, the order of the orthogonal
projections of the vertices of P_{uw} on l_{uw} is the same as the order they
appear in P_{uw}.)
The problem of finding monotone drawings for trees has been studied in
several recent papers. The main focus is to reduce the size of the drawing.
Currently, the smallest drawing size is O(n^{1.205}) x O(n^{1.205}). In this
paper, we present an algorithm for constructing monotone drawings of trees on a
grid of size at most 12n x 12n. The smaller drawing size is achieved by a new
simple Path Draw algorithm, and a procedure that carefully assigns primitive
vectors to the paths of the input tree T.
We also show that there exists a tree T_0 such that any monotone drawing of
T_0 must use a grid of size Omega(n) x Omega(n). So the size of our monotone
drawing of trees is asymptotically optimal
A note on the maximal out-degree of Galton-Watson trees
In this note we consider both the local maximal out-degree and the global
maximal out-degree of Galton-Watson trees. In particular, we show that the tail
of any local maximal out-degree and that of the offspring distribution are
asymptotically of the same order. However for the global maximal out-degree,
this is only true in the subcritical case.Comment: 7 page
On W_2 lifting of Frobenius of Algebraic Surfaces
We completely decide which minimal algebraic surfaces in positive
characteristics allow a lifting of their Frobenius over the trucated witt rings
of lengh 2.Comment: 10 pages. Comments are welcom
Allowed parameter regions for a general inflation moded
The early Universe inflation is well known as a promising theory to explain
the origin of large scale structure of Universe and to solve the early universe
pressing problems. For a resonable inflation model, the potential during
inflation must be very flat in, at least, the direction of the inflaton. To
construct the inflaton potential all the known related astrophysics
observations should be included. For a general tree-level hybrid inflation
potential, which is not discussed fully so far, the parameters in it are shown
how to be constrained via the astrophysics data observed and to be obtained to
the expected accuracy, and consistent cosmology requirements.Comment: 5 figs, Late
A dynamical mechanism for generating quark confinement
We explore the dynamical mechanism for generating the infrared singular
quark-gluon vertex and quark confinement based on the gauge invariance in
covariant-gauge quantum chromodynamics(QCD). We first derive the
gauge-invariance constraint relation for the infrared-limit behavior of the
quark-gluon vertex, which shows the mechanism for generating the infrared
behavior of the quark-gluon vertex. We hence unravel a novel mechanism for
generating an infrared singular quark-gluon vertex and then a linear rising
potential for confining massive quarks, where the infrared singularity in the
form factors composing the quark-ghost scattering kernel plays a crucial role.
The mechanism for linking chiral symmetry breaking with quark confinement is
also shown
Particle Physics Inflation Model Constrained from Astrophysics Observations
The early Universe inflation is well known as a promising theory to explain
the origin of large scale structure of the Universe, a causal theory for the
origin of primordial density fluctuations which may explain the observed
density inhomogeneities and cosmic microwave fluctuations in the very early
Universe, and to solve the early universe pressing problems for the standard
hot big bang theory. For a resonable inflation model, the potential during
inflation must be very flat in, at least, the direction of the inflaton. To
construct a resonable inflation model, or the inflaton potential, all the known
related astrophysics observations should be included. For a general tree-level
hybrid inflation potential, which is not discussed fully so far for the quartic
term, the parameters in it are shown how to be constrained via the astrophysics
data observed and to be obtained to the expected accuracy by the soon lauched
MAP and PLANCK satellite missions, as well as the consistent cosmology
requirements. We find the effective inflaton mass parameter is in the TeV
range, and the quartic term's self-coupling constant tiny, needs fine-tunning.Comment: 10 page
Nonperturbative Fermion-Boson Vertex Function in Gauge Theories
The nonperturbative fermion-boson vertex function in four-dimensional Abelian
gauge theories is self-consistently and exactly derived in terms of a complete
set of normal (longitudinal) and transverse Ward-Takahashi relations for the
The nonperturbative fermion-boson vertex function in four-dimensional Abelian
gauge theories is self-consistently and exactly derived in terms of a complete
set of normal(longitudinal) and transverse Ward-Takahashi relations for the
fermion-boson and the axial-vector vertices in the case of massless fermion, in
which the possible quantum anomalies and perturbative corrections are taken
into account simultaneously. We find that this nonperturbative fermion-boson
vertex function is expressed nonperturbatively in terms of the full fermion
propagator and contains the contributions of the transverse axial anomaly and
perturbative corrections. The result that the transverse axial anomaly
contributes to the nonperturbative fermion-boson vertex arises from the
coupling between the fermion-boson and the axial-vector vertices through the
transverse Ward-Takahashi relations for them and is a consequence of gauge
invariance.Comment: 11 pages, RevTa
Transverse Ward-Takahashi Relation for the Fermion-Boson Vertex Function in 4-dimensional QED
I present a general expression of the transverse Ward-Takahashi relation for
the fermion-boson vertex function in momentum space in 4-dimensional QED, from
which the corresponding one-loop expression is derived straightforwardly. Then
I deduce carefully this transverse Ward-Takahashi relation to one-loop order in
d-dimensions, with . The result shows that this relation in
d-dimensions has the same form as one given in 4-dimensions and there is no
need for an additional piece proportional to to include for this
relation to hold in 4-dimensions. This result is confirmed by an explicit
computation of terms in this transverse WT relation to one-loop order. I also
make some comments on the paper given by Pennington and Williams who checked
the transverse Ward-Takahashi relation at one loop order in d-dimensions.Comment: 15 page
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