101,615 research outputs found
Local matching indicators for transport problems with concave costs
In this paper, we introduce a class of indicators that enable to compute
efficiently optimal transport plans associated to arbitrary distributions of N
demands and M supplies in R in the case where the cost function is concave. The
computational cost of these indicators is small and independent of N. A
hierarchical use of them enables to obtain an efficient algorithm
Local matching indicators for transport with concave costs
In this note, we introduce a class of indicators that enable to compute
efficiently optimal transport plans associated to arbitrary distributions of
demands and supplies in in the case where the cost
function is concave. The computational cost of these indicators is small and
independent of . A hierarchical use of them enables to obtain an efficient
algorithm
Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
We study dynamical optimal transport metrics between density matrices
associated to symmetric Dirichlet forms on finite-dimensional -algebras.
Our setting covers arbitrary skew-derivations and it provides a unified
framework that simultaneously generalizes recently constructed transport
metrics for Markov chains, Lindblad equations, and the Fermi
Ornstein--Uhlenbeck semigroup. We develop a non-nommutative differential
calculus that allows us to obtain non-commutative Ricci curvature bounds,
logarithmic Sobolev inequalities, transport-entropy inequalities, and spectral
gap estimates
An overview on the proof of the splitting theorem in non-smooth context
We give a quite detailed overview on the proof of the Cheeger-Colding-Gromoll
splitting theorem in the abstract framework of spaces with Riemannian Ricci
curvature bounded from below.Comment: 52 page
The Abresch-Gromoll inequality in a non-smooth setting
We prove that the Abresch-Gromoll inequality holds on infinitesimally
Hilbertian CD(K,N) spaces in the same form as the one available on smooth
Riemannian manifolds
Variable-range hopping in 2D quasi-1D electronic systems
A semi-phenomenological theory of variable-range hopping (VRH) is developed
for two-dimensional (2D) quasi-one-dimensional (quasi-1D) systems such as
arrays of quantum wires in the Wigner crystal regime. The theory follows the
phenomenology of Efros, Mott and Shklovskii allied with microscopic arguments.
We first derive the Coulomb gap in the single-particle density of states,
, where is the energy of the charge excitation. We then
derive the main exponential dependence of the electron conductivity in the
linear (L), {\it i.e.} , and current
in the non-linear (NL), {\it i.e.} , response regimes ( is the
applied electric field). Due to the strong anisotropy of the system and its
peculiar dielectric properties we show that unusual, with respect to known
results, Coulomb gaps open followed by unusual VRH laws, {\it i.e.} with
respect to the disorder-dependence of and and the
values of and .Comment: (v2) Entirely re-written (some notations changed, new presentation
and new structure). Part on the Wigner crystal taken off for short. Minor
changes in results. 16 RevTex4 pages, 5 figures. (v3) Published versio
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