Results 1  10
of
1,395
Shape fluctuations and random matrices
, 1999
"... We study a certain random growth model in two dimensions closely related to the onedimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the TracyWidom largest eigenvalue distribution for the Gaussian Uni ..."
Abstract

Cited by 240 (10 self)
 Add to MetaCart
We study a certain random growth model in two dimensions closely related to the onedimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the TracyWidom largest eigenvalue distribution for the Gaussian Unitary Ensemble (GUE).
A geometrical inverse problem
, 1986
"... A simple solution is given to the problem of finding the unknown boundary from the extra boundary condition. ..."
Abstract

Cited by 155 (118 self)
 Add to MetaCart
A simple solution is given to the problem of finding the unknown boundary from the extra boundary condition.
Chern–Simons Perturbation Theory
 II,” J. Diff. Geom
, 1994
"... Abstract. We study the perturbation theory for three dimensional Chern–Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the action obtained by BRS gauge fixing in the Lorentz gauge has a superspace formulation. The bas ..."
Abstract

Cited by 124 (2 self)
 Add to MetaCart
Abstract. We study the perturbation theory for three dimensional Chern–Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the action obtained by BRS gauge fixing in the Lorentz gauge has a superspace formulation. The basic properties of the propagator and the Feynman rules are written in a precise manner in the language of differential forms. Using the explicit description of the propagator singularities, we prove that the theory is finite. Finally the anomalous metric dependence of the 2loop partition function on the Riemannian metric (which was introduced to define the gauge fixing) can be cancelled by a local counterterm as in the 1loop case [28]. In fact, the counterterm is equal to the Chern–Simons action of the metric connection, normalized precisely as one would expect based on the framing dependence of Witten’s exact solution.
A "universal" Construction Of Artstein's Theorem On Nonlinear Stabilization
 Systems & Control Letters
, 1989
"... This note presents an explicit proof of the theorem due to Artstein which states that the existence of a smooth controlLyapunov function implies smooth stabilizability. Moreover, the result is extended to the realanalytic and rational cases as well. The proof uses a "universal" formula given b ..."
Abstract

Cited by 113 (17 self)
 Add to MetaCart
This note presents an explicit proof of the theorem due to Artstein which states that the existence of a smooth controlLyapunov function implies smooth stabilizability. Moreover, the result is extended to the realanalytic and rational cases as well. The proof uses a "universal" formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation. Rutgers Center for Systems and Control February 1989 1 Keywords: Smooth stabilization, Artstein's Theorem. 2 Research supported in part by US Air Force Grant 880235 1 Introduction The main object of this note is to provide a simple, explicit, and in a sense "universal" proof of a result due to Artstein ([1]), and to obtain certain generalizations of it. The result concerns control systems of the type x(t) = f(x(t)) + u 1 (t)g 1 (x(t)) + : : : + um (t)g m (x(t)) (1) with states x(t) 2 IR n and controls u(t) = (u 1 (t); : : : ; um (t)) 2 IR m , where f as well as the ...
A proof of the Kepler conjecture
 Math. Intelligencer
, 1994
"... This section describes the structure of the proof of ..."
Abstract

Cited by 112 (11 self)
 Add to MetaCart
This section describes the structure of the proof of
Microlocal analysis and interacting quantum field theory: Renormalizability of ϕ 4
 Operator Algebras and Quantum Field Theory. Proceedings
, 1996
"... Dedicated to the memory of Professor Roberto Stroffolini Abstract. We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) spacetimes. We develop a purely local version of the StückelbergBogoliubovEpsteinGlaser method of renormalization ..."
Abstract

Cited by 92 (15 self)
 Add to MetaCart
Dedicated to the memory of Professor Roberto Stroffolini Abstract. We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) spacetimes. We develop a purely local version of the StückelbergBogoliubovEpsteinGlaser method of renormalization by using techniques from microlocal analysis. Relying on recent results of Radzikowski, Köhler and the authors about a formulation of a local spectrum condition in terms of wave front sets of correlation functions of quantum fields on curved spacetimes, we construct timeordered operatorvalued products of Wick polynomials of free fields. They serve as building blocks for a local (perturbative) definition of interacting fields. Renormalization in this framework amounts to extensions of expectation values of timeordered products to all points of spacetime. The extensions are classified according to a microlocal generalization of Steinmann scaling degree corresponding to the degree of divergence in other renormalization schemes. As a result, we prove that the usual perturbative classification of interacting quantum
Global wellposedness, scattering, and blowup for the energycritical, focusing, nonlinear Schrödinger equation in the radial case
, 2006
"... ..."
Toeplitz Quantization Of Kähler Manifolds And gl(N), N → ∞ Limits
"... For general compact Kähler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a welldefined (by operator norm estimates) classical limit. This generalizes earlier results of the authors and Klimek and Lesniewski obtained for the torus and higher genus Riemann s ..."
Abstract

Cited by 84 (10 self)
 Add to MetaCart
For general compact Kähler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a welldefined (by operator norm estimates) classical limit. This generalizes earlier results of the authors and Klimek and Lesniewski obtained for the torus and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finitedimensional matrix algebras gl(N), N → ∞.
Modular Operads
 COMPOSITIO MATH
, 1994
"... We develop a "higher genus" analogue of operads, which we call modular operads, in which graphs replace trees in the definition. We study a functor F on the category of modular operads, the Feynman transform, which generalizes Kontsevich's graph complexes and also the bar construction for operads. ..."
Abstract

Cited by 68 (5 self)
 Add to MetaCart
We develop a "higher genus" analogue of operads, which we call modular operads, in which graphs replace trees in the definition. We study a functor F on the category of modular operads, the Feynman transform, which generalizes Kontsevich's graph complexes and also the bar construction for operads. We calculate the Euler characteristic of the Feynman transform, using the theory of symmetric functions: our formula is modelled on Wick's theorem. We give applications to the theory of moduli spaces of pointed algebraic curves.