1,041 research outputs found
Gaussian limits for multidimensional random sequential packing at saturation (extended version)
Consider the random sequential packing model with infinite input and in any
dimension. When the input consists of non-zero volume convex solids we show
that the total number of solids accepted over cubes of volume is
asymptotically normal as . We provide a rate of
approximation to the normal and show that the finite dimensional distributions
of the packing measures converge to those of a mean zero generalized Gaussian
field. The method of proof involves showing that the collection of accepted
solids satisfies the weak spatial dependence condition known as stabilization.Comment: 31 page
Magnetism, FeS colloids, and Origins of Life
A number of features of living systems: reversible interactions and weak
bonds underlying motor-dynamics; gel-sol transitions; cellular connected
fractal organization; asymmetry in interactions and organization; quantum
coherent phenomena; to name some, can have a natural accounting via
interactions, which we therefore seek to incorporate by expanding the horizons
of `chemistry-only' approaches to the origins of life. It is suggested that the
magnetic 'face' of the minerals from the inorganic world, recognized to have
played a pivotal role in initiating Life, may throw light on some of these
issues. A magnetic environment in the form of rocks in the Hadean Ocean could
have enabled the accretion and therefore an ordered confinement of
super-paramagnetic colloids within a structured phase. A moderate H-field can
help magnetic nano-particles to not only overcome thermal fluctuations but also
harness them. Such controlled dynamics brings in the possibility of accessing
quantum effects, which together with frustrations in magnetic ordering and
hysteresis (a natural mechanism for a primitive memory) could throw light on
the birth of biological information which, as Abel argues, requires a
combination of order and complexity. This scenario gains strength from
observations of scale-free framboidal forms of the greigite mineral, with a
magnetic basis of assembly. And greigite's metabolic potential plays a key role
in the mound scenario of Russell and coworkers-an expansion of which is
suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed
Krishnaswami Alladi, Springer 201
Random parking, Euclidean functionals, and rubber elasticity
We study subadditive functions of the random parking model previously
analyzed by the second author. In particular, we consider local functions
of subsets of and of point sets that are (almost) subadditive in
their first variable. Denoting by the random parking measure in
, and by the random parking measure in the cube
, we show, under some natural assumptions on , that there
exists a constant such that % % almost surely. If is the counting measure of in , then we
retrieve the result by the second author on the existence of the jamming limit.
The present work generalizes this result to a wide class of (almost)
subadditive functions. In particular, classical Euclidean optimization problems
as well as the discrete model for rubber previously studied by Alicandro,
Cicalese, and the first author enter this class of functions. In the case of
rubber elasticity, this yields an approximation result for the continuous
energy density associated with the discrete model at the thermodynamic limit,
as well as a generalization to stochastic networks generated on bounded sets.Comment: 28 page
Weighted second-order Poincaré inequalities: Application to RSA models
Consider an ergodic stationary random field A on the ambient space R d. In a recent work we introduced the notion of weighted (first-order) functional inequalities , which extend standard functional inequalities like spectral gap, covariance, and logarithmic Sobolev inequalities, while still ensuring strong concentration properties. We also developed a constructive approach to these weighted inequalities, proving their validity for prototypical examples like Gaussian fields with arbitrary covariance function , Voronoi and Delaunay tessellations of Poisson point sets, and random sequential adsorption (RSA) models, which do not satisfy standard functional inequalities. In the present contribution, we turn to second-order Poincaré inequalities à la Chatterjee: while first-order inequalities quantify the distance to constants for nonlinear functions X(A) in terms of their local dependence on the random field A, second-order inequalities quantify their distance to normality. For the above-mentioned examples, we prove the validity of suitable weighted second-order Poincaré inequalities. Applied to RSA models, these functional inequalities allow us to complete and improve previous results by Schreiber, Penrose, and Yukich on the jamming limit, and to propose and fully analyze a more efficient algorithm to approximate the latter
Quantification of uncertainty in coarse-scale relative permeability for reservoir production forecast
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