The Scaling Limit Of The Correlation Of Holes On The Triangular Lattice With Periodic Boundary Conditions
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The Scaling Limit Of The Correlation Of Holes On The Triangular Lattice With Periodic Boundary Conditions
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Author : Mihai Ciucu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-10
The Scaling Limit Of The Correlation Of Holes On The Triangular Lattice With Periodic Boundary Conditions written by Mihai Ciucu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-10 with Science categories.
The author defines the correlation of holes on the triangular lattice under periodic boundary conditions and studies its asymptotics as the distances between the holes grow to infinity. He proves that the joint correlation of an arbitrary collection of triangular holes of even side-lengths (in lattice spacing units) satisfies, for large separations between the holes, a Coulomb law and a superposition principle that perfectly parallel the laws of two dimensional electrostatics, with physical charges corresponding to holes, and their magnitude to the difference between the number of right-pointing and left-pointing unit triangles in each hole. The author details this parallel by indicating that, as a consequence of the results, the relative probabilities of finding a fixed collection of holes at given mutual distances (when sampling uniformly at random over all unit rhombus tilings of the complement of the holes) approach, for large separations between the holes, the relative probabilities of finding the corresponding two dimensional physical system of charges at given mutual distances. Physical temperature corresponds to a parameter refining the background triangular lattice. He also gives an equivalent phrasing of the results in terms of covering surfaces of given holonomy. From this perspective, two dimensional electrostatic potential energy arises by averaging over all possible discrete geometries of the covering surfaces.
The Scaling Limit Of The Correlation Of Holes On The Triangular Lattice With Periodic Boundary Conditions
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Author : Mihai Ciucu
language : en
Publisher:
Release Date : 2009
The Scaling Limit Of The Correlation Of Holes On The Triangular Lattice With Periodic Boundary Conditions written by Mihai Ciucu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Bethe-ansatz technique categories.
A Random Tiling Model For Two Dimensional Electrostatics
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Author : Mihai Ciucu
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
A Random Tiling Model For Two Dimensional Electrostatics written by Mihai Ciucu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Studies the correlation of holes in random lozenge (i.e., unit rhombus) tilings of the triangular lattice. This book analyzes the joint correlation of these triangular holes when their complement is tiled uniformly at random by lozenges.
The Dynamics Of Modulated Wave Trains
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Author : A. Doelman
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
The Dynamics Of Modulated Wave Trains written by A. Doelman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The authors investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg-Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine-Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh-Nagumo equation and to hydrodynamic stability problems.
Holder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension Three
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Author : Robert C. Dalang
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-10
Holder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension Three written by Robert C. Dalang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-10 with Mathematics categories.
The authors study the sample path regularity of the solution of a stochastic wave equation in spatial dimension $d=3$. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. The authors prove that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any fixed $x\in\mathbb{R}^3$, the sample paths in time are Holder continuous functions. Further, the authors obtain joint Holder continuity in the time and space variables. Their results rely on a detailed analysis of properties of the stochastic integral used in the rigourous formulation of the s.p.d.e., as introduced by Dalang and Mueller (2003). Sharp results on one- and two-dimensional space and time increments of generalized Riesz potentials are a crucial ingredient in the analysis of the problem. For spatial covariances given by Riesz kernels, the authors show that the Holder exponents that they obtain are optimal.
Scattering Resonances For Several Small Convex Bodies And The Lax Phillips Conjecture
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Author : Luchezar N. Stoyanov
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Scattering Resonances For Several Small Convex Bodies And The Lax Phillips Conjecture written by Luchezar N. Stoyanov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean space. The class of obstacles of this type which is considered are contained in a given (large) ball and have some additional properties.
Unfolding Cr Singularities
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Author : Adam Coffman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Unfolding Cr Singularities written by Adam Coffman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 205, number 962 (first of 5 numbers)."
Random Sets And Invariants For Type Ii Continuous Tensor Product Systems Of Hilbert Spaces
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Author : Volkmar Liebscher
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-10
Random Sets And Invariants For Type Ii Continuous Tensor Product Systems Of Hilbert Spaces written by Volkmar Liebscher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-10 with Mathematics categories.
In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying $E_0$-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in $[0,1]$ or $\mathbb R_+$. These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types $\mathrm{I}_n$, $\mathrm{II}_n$ and $\mathrm{III}$ is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.
Approximate Homotopy Of Homomorphisms From C X Into A Simple C Algebra
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Author : Huaxin Lin
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Approximate Homotopy Of Homomorphisms From C X Into A Simple C Algebra written by Huaxin Lin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 205, number 963 (second of 5 numbers)."
On A Conjecture Of E M Stein On The Hilbert Transform On Vector Fields
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Author : Michael Thoreau Lacey
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
On A Conjecture Of E M Stein On The Hilbert Transform On Vector Fields written by Michael Thoreau Lacey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 205, number 965 (fourth of 5 numbers)."