Results 1  10
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106
Geometric Ergodicity and Hybrid Markov Chains
, 1997
"... Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the socalled hybrid ..."
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Cited by 107 (29 self)
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Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the socalled hybrid chains. We prove that under certain conditions, a hybrid chain will "inherit" the geometric ergodicity of its constituent parts. 1 Introduction A question of increasing importance in the Markov chain Monte Carlo literature (Gelfand and Smith, 1990; Smith and Roberts, 1993) is the issue of geometric ergodicity of Markov chains (Tierney, 1994, Section 3.2; Meyn and Tweedie, 1993, Chapters 15 and 16; Roberts and Tweedie, 1996). However, there are a number of different notions of the phrase "geometrically ergodic", depending on perspective (total variation distance vs. in L 2 ; with reference to a particular V function; etc.). One goal of this paper is to review and clarify the relationship...
A minimaxprinciple for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials
 8] Ira W. Herbst. Spectral theory of the operator (p2 + m2)1/2  Ze2/r.Comm. Math. Phys
, 1999
"... Aminimax principle is derived for the eigenvalues in the spectral gap of a possibly nonsemibounded selfadjoint operator. It allows the nth eigenvalue of the Dirac operator with Coulomb potential from below to be bound by the nth eigenvalue of a semibounded Hamiltonian which is of interest in the c ..."
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Cited by 46 (6 self)
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Aminimax principle is derived for the eigenvalues in the spectral gap of a possibly nonsemibounded selfadjoint operator. It allows the nth eigenvalue of the Dirac operator with Coulomb potential from below to be bound by the nth eigenvalue of a semibounded Hamiltonian which is of interest in the context of stability of matter. As a second application it is shown that the Dirac operator with suitable nonpositive potential has at least as many discrete eigenvalues as the Schro $ dinger operator with the same potential. 1.
Oneparticle (improper) states in Nelson's massless model
, 2002
"... In the oneparticle sector of Nelson's massless model, the oneparticle states are constructed for an arbitrarily small infrared cuto in the interaction term of the Hamiltonian of the system. The performed method is a constructive one which exploits only regular perturbation theory, by a suita ..."
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Cited by 34 (5 self)
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In the oneparticle sector of Nelson's massless model, the oneparticle states are constructed for an arbitrarily small infrared cuto in the interaction term of the Hamiltonian of the system. The performed method is a constructive one which exploits only regular perturbation theory, by a suitable iteration scheme. The disappearance of oneparticle states is showed in the limit of no infrared regularization. Constructive features, as regularity in some parameters, are also inquired.
Nonvariational approximation of discrete eigenvalues of selfadjoint operators
 IMA J. Numer. Anal
"... Abstract. We establish sufficiency conditions in order to achieve approximation to discrete eigenvalues of selfadjoint operators in the secondorder projection method suggested recently by Levitin and Shargorodsky, [15]. We find explicit estimates for the eigenvalue error and study in detail two co ..."
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Cited by 23 (8 self)
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Abstract. We establish sufficiency conditions in order to achieve approximation to discrete eigenvalues of selfadjoint operators in the secondorder projection method suggested recently by Levitin and Shargorodsky, [15]. We find explicit estimates for the eigenvalue error and study in detail two concrete model examples. Our results show that, unlike the majority of the standard methods, secondorder projection strategies combine nonpollution and approximation at a very high level of generality. 1.
Scattering of an Infraparticle: The One Particle Sector
 in Nelsons Massless Model. Annales Henri Poincar 6, Issue: 3, 553  606
, 2005
"... Abstract. In the oneparticle sector of Nelson’s massless model, we construct scattering states in the timedependent approach. On the sodefined scattering subspaces, the convergence of the asymptotic Weyl operators related to the boson field as well as the asymptotic limit of the mean velocity of ..."
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Cited by 22 (2 self)
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Abstract. In the oneparticle sector of Nelson’s massless model, we construct scattering states in the timedependent approach. On the sodefined scattering subspaces, the convergence of the asymptotic Weyl operators related to the boson field as well as the asymptotic limit of the mean velocity of the infraparticle are established. The construction relies on some spectral results concerning the oneparticle (improper) states of the system. Moreover, in the region of physical interest, we assume a positive bound from below for the second derivative of the ground state energy as a function of the total momentum, uniform in the limit of no infrared cutoff in the interaction term.
Transient electromagnetic wave propagation in anisotropic dispersive media
 J. Opt. Soc. Am. A
, 1993
"... This paper focuses on propagation of transient electromagnetic waves in waveguides of general cross section with perfectly conducting walls. The solution of the transient wave propagation problem relies on a wave splitting technique, which has been frequently used in direct and inverse scattering p ..."
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Cited by 21 (3 self)
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This paper focuses on propagation of transient electromagnetic waves in waveguides of general cross section with perfectly conducting walls. The solution of the transient wave propagation problem relies on a wave splitting technique, which has been frequently used in direct and inverse scattering problems during the last decade. The field in the waveguide is represented as a time convolution of a Green function and the excitation. Some numerical computations illustrate the method. A new way of calculating the first precursor in a Lorentz medium is presented. This method, which is not based upon the classical asymptotic methods, gives an expression of the first precursor at all depths in the medium. The excitation of the waveguide modes for time dependent sources is also addressed. 1
DECAY PROPERTIES OF SPECTRAL PROJECTORS WITH APPLICATIONS TO ELECTRONIC STRUCTURE
, 2010
"... Motivated by applications in quantum chemistry and solid state physics, we apply general results from approximation theory and matrix analysis to the study of the decay properties of spectral projectors associated with large and sparse Hermitian matrices. Our theory leads to a rigorous proof of the ..."
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Cited by 18 (3 self)
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Motivated by applications in quantum chemistry and solid state physics, we apply general results from approximation theory and matrix analysis to the study of the decay properties of spectral projectors associated with large and sparse Hermitian matrices. Our theory leads to a rigorous proof of the exponential offdiagonal decay (‘nearsightedness’) for the density matrix of gapped systems at zero electronic temperature in both orthogonal and nonorthogonal representations, thus providing a firm theoretical basis for the possibility of linear scaling methods in electronic structure calculations for nonmetallic systems. Our theory also allows us to treat the case of density matrices for arbitrary systems at finite electronic temperature, including metals. Other possible applications are also discussed.
Nonperturbative Mass and Charge Renormalization in Relativistic Nophoton QED
 Commun. Math. Phys
"... Abstract. Starting from a formal Hamiltonian as found in the physics literature – omitting photons – we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the oneelectron subspace is welldefined. Our construction is nonperturbative and does n ..."
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Cited by 16 (8 self)
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Abstract. Starting from a formal Hamiltonian as found in the physics literature – omitting photons – we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the oneelectron subspace is welldefined. Our construction is nonperturbative and does not use a cutoff. The Hamiltonian is relevant for the description of the Lamb shift in muonic atoms. 1.
Asymptotic Variance and Convergence Rates of NearlyPeriodic MCMC Algorithms
, 2001
"... We consider nearlyperiodic chains, which may have excellent functionalestimation properties but poor distributional convergence rate. We show how simple modications of the chain (involving using a random number of iterations) can greatly improve the distributional convergence of the chain. We prov ..."
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Cited by 15 (3 self)
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We consider nearlyperiodic chains, which may have excellent functionalestimation properties but poor distributional convergence rate. We show how simple modications of the chain (involving using a random number of iterations) can greatly improve the distributional convergence of the chain. We prove various theoretical results about convergence rates of the modied chains. We also consider a number of examples. 1.