Universality for mathematical and physical systems

By Percy Deift. 2006

139 citations recorded by the source corpus.

PCT No. PCT/BR89/00011 Sec. 371 Date Feb. 12, 1991 Sec. 102(e) Date Feb. 12, 1991 PCT Filed Aug. 17, 1989 PCT Pub. No. WO90/03770 PCT Pub. Date Apr. 19, 1990.The present invention relates to a therapeutic table for the treatment of spinal ailments which consists of a horizontal platform or table divided into three segments. An upper segment supports the patient's torso and head, a center segment supports the pelvic region of the patient and a lower segment supports the legs of the patient. The patient, while lying on his or her back, is securedly strapped to the upper and center segments, whereupon the center segment is caused to move upward diagonally at approximately a 45 degree angle. This linear, angled motion, which is reciprocally repeated, results in simultaneous arching and tractioning of the patient's spine, thereby decompressing the vertebrae and providing therapeutic treatment.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/959460ddd81bedd2efd26b2f06c347a3e3ad8104

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Sparse regular random graphs: Spectral density and eigenvectors (2009, background): “In the last couple of decades there has been an enormous amount of activity in the study of universal properties of random matrices, inspired by their connection to (universal) physical systems.”
The Distributions of Random Matrix Theory and their Applications (2009, background): “Deift’s ICM 2006 lecture [7] is a recommended overview for these developments.”
Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge (2009, background): “(See [6] for an extended discussion of the universality phenomenon, and [27] for further references on universality results in the context of Wigner Hermitian matrices.”
Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results (2012, result): “The result in [BDJ] was the first of many results linking problems in pure and applied mathematics and in physics to the Tracy-Widom distribution F2(t) and its symplectic and orthogonal analogs (see, for example [Dei2]).”
Eigenvalue statistics for CMV matrices: From Poisson to clock via random matrix ensembles (2009, background): “This theorem demonstrates that (at least for this model) the transition from Poisson to Clock statistics passes through a continuum of intermediate processes.”
TAIL BOUNDS FOR ALL EIGENVALUES OF A SUM OF RANDOM MATRICES (2011, background): “They further observed the phenomenon of universality : as the dimension increases, the spectral statistics become independent of the distribution of the random matrix; instead, they are determined by the symmetries of the distribution [Dei07].”
High Dimensional Statistical Inference and Random Matrices (2006, background): “he Vandermonde term in (4). The fact that the same limit arises in the single and double Wishart settings (Laguerre, Jacobi ensembles) is an instance of the universality discussed in P. Deift’s paper [29] in this volume. In a diﬀerent direction, one can modify the 1At time of writing, for available ”
Tropical Combinatorics and Whittaker functions (2011, background): “, 1, 19, 49]. The RSK correspondence provides a concrete connection between these areas and large classes of canonical models studied in probability as well asstatisticalandsoft-condensedmatterphysics[30, 34, 40]. Infact, muchofthe progressin understandingthe statistical properties of the Kardar-Par”
A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, background): “3 For an introduction to the idea of universality from a mathematical perspective, see [34].”