THE CORNER TRANSFER MATRIX OF SOME FREE-FERMION SYSTEMS AND MEIXNER’S POLYNOMIALS

1990 ◽  
Vol 04 (05) ◽  
pp. 895-905 ◽  
Author(s):  
T.T. TRUONG ◽  
I. PESCHEL
Keyword(s):  
Asymptotic Behavior ◽  
Orthogonal Polynomials ◽  
Special Class ◽  
Finite Lattice ◽  
Free Fermion ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Meixner Polynomials ◽  
Fermion Systems ◽  
Large Lattice

Corner transfer matrices of some free-fermion vertex systems on a finite lattice, are exactly diagonalised in the Hamiltonian limit with the help of a special class of orthogonal polynomials: the Meixner polynomials. We present the derivation, discuss the asymptotic behavior for a large lattice and compare the results with numerical computation.

scholarly journals Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 180
Author(s):  
Oleg Avsyankin
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Integral Equations ◽  
Spherical Harmonics ◽  
Special Class ◽  
Continuous Functions ◽  
Asymptotic Behavior Of Solutions ◽  
Free Term ◽  
Research Technique ◽  
Multidimensional Integral

The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.

scholarly journals LOWERING AND RAISING OPERATORS FOR THE FREE MEIXNER CLASS OF ORTHOGONAL POLYNOMIALS

2009 ◽  
Vol 12 (03) ◽  
pp. 387-399 ◽  
Author(s):  
EUGENE LYTVYNOV ◽  
IRINA RODIONOVA
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
Meixner Polynomials ◽  
The Real ◽  
Raising Operators ◽  
Meixner Class

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line.

Application of Stieltjes theory for S-fractions to birth and death processes

1983 ◽  
Vol 15 (03) ◽  
pp. 507-530 ◽  
Author(s):  
G. Bordes ◽  
B. Roehner
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bound ◽  
Special Class ◽  
Jacobi Matrix ◽  
General Theorem ◽  
Sufficient Conditions ◽  
Death Process ◽  
Nearest Neighbour ◽  
Birth And Death Process ◽  
Birth And Death Processes

We are interested in obtaining bounds for the spectrum of the infinite Jacobi matrix of a birth and death process or of any process (with nearest-neighbour interactions) defined by a similar Jacobi matrix. To this aim we use some results of Stieltjes theory for S-fractions, after reviewing them. We prove a general theorem giving a lower bound of the spectrum. The theorem also gives sufficient conditions for the spectrum to be discrete. The expression for the lower bound is then worked out explicitly for several, fairly general, classes of birth and death processes. A conjecture about the asymptotic behavior of a special class of birth and death processes is presented.

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