22 research outputs found
Multidimensional sticky Brownian motions as limits of exclusion processes
We study exclusion processes on the integer lattice in which particles change
their velocities due to stickiness. Specifically, whenever two or more
particles occupy adjacent sites, they stick together for an extended period of
time, and the entire particle system is slowed down until the ``collision'' is
resolved. We show that under diffusive scaling of space and time such processes
converge to what one might refer to as a sticky reflected Brownian motion in
the wedge. The latter behaves as a Brownian motion with constant drift vector
and diffusion matrix in the interior of the wedge, and reflects at the boundary
of the wedge after spending an instant of time there. In particular, this leads
to a natural multidimensional generalization of sticky Brownian motion on the
half-line, which is of interest in both queuing theory and stochastic portfolio
theory. For instance, this can model a market, which experiences a slowdown due
to a major event (such as a court trial between some of the largest firms in
the market) deciding about the new market leader.Comment: Published at http://dx.doi.org/10.1214/14-AAP1019 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Can one hear the shape of a population history?
Reconstructing past population size from present day genetic data is a major
goal of population genetics. Recent empirical studies infer population size
history using coalescent-based models applied to a small number of individuals.
Here we provide tight bounds on the amount of exact coalescence time data
needed to recover the population size history of a single, panmictic population
at a certain level of accuracy. In practice, coalescence times are estimated
from sequence data and so our lower bounds should be taken as rather
conservative.Comment: 22 pages, 7 figures; v2 is significantly revised from v
On the influence of the seed graph in the preferential attachment model.
Abstract We study the influence of the seed graph in the preferential attachment model, focusing on the case of trees. We first show that the seed has no effect from a weak local limit point of view. On the other hand, we conjecture that different seeds lead to different distributions of limiting trees from a total variation point of view. We take a first step in proving this conjecture by showing that seeds with different degree profiles lead to different limiting distributions for the (appropriately normalized) maximum degree, implying that such seeds lead to different (in total variation) limiting trees
Common Genetic Variants of the Human Steroid 21-Hydroxylase Gene (CYP21A2) Are Related to Differences in Circulating Hormone Levels
This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Hungarian Scientific Research Fund (OTKA, PD100648 (AP)) Technology Innovation Fund, National Developmental Agency (KTIA-AIK-2012-12-1-0010). AP is the recipient of a “Lendület” grant from the Hungarian Academy of Sciences
On the Influence of the Seed Graph in the Preferential Attachment Model
We study the influence of the seed graph in the preferential attachment
model, focusing on the case of trees. We first show that the seed has no effect
from a weak local limit point of view. On the other hand, we conjecture that
different seeds lead to different distributions of limiting trees from a total
variation point of view. We take a first step in proving this conjecture by
showing that seeds with different degree profiles lead to different limiting
distributions for the (appropriately normalized) maximum degree, implying that
such seeds lead to different (in total variation) limiting trees