567 research outputs found
Dynamics of a system of sticking particles of a finite size on the line
The continuous limit of large systems of particles of finite size on the line
is described. The particles are assumed to move freely and stick under
collision, to form compound particles whose mass and size is the sum of the
masses and sizes of the particles before collision, and whose velocity is
determined by conservation of linear momentum.Comment: 15 page
From optimal transportation to optimal teleportation
The object of this paper is to study estimates of
for small . Here is
the Wasserstein metric on positive measures, , is a probability
measure and a signed, neutral measure (). In [W1] we proved
uniform (in ) estimates for provided can be
controlled in terms of the , for any smooth
function .
In this paper we extend the results to the case where such a control fails.
This is the case where if, e.g. has a disconnected support, or if the
dimension of , (to be defined) is larger or equal .
In the later case we get such an estimate provided for
. If we get a log-Lipschitz estimate.
As an application we obtain H\"{o}lder estimates in for curves of
probability measures which are absolutely continuous in the total variation
norm .
In case the support of is disconnected (corresponding to ) we
obtain sharp estimates for ("optimal teleportation"): where is expressed in terms of optimal
transport on a metric graph, determined only by the relative distances between
the connected components of the support of , and the weights of the
measure in each connected component of this support.Comment: 24 pages, 3 figure
- …