On determinants of Toeplitz-Hessenberg matrices arising in power series

Inselberg, Alfred

doi:10.1016/0022-247x(78)90080-x

Cited by 18 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where a 0 = 0 and a k = 0 for at least one k > 0, is called a lower Toeplitz-Hessenberg matrix. This class of matrix have been encountered in many scientific and engineering applications (see, among others, [1,[13][14][15][16] and related references therein).…”

Section: Toeplitz-hessenberg Determinants and Formulas For Their Evaluationmentioning

confidence: 99%

A note on Pell-Padovan numbers and their connection with Fibonacci numbers

Goy

Sharyn

2020

Carpathian Math. Publ.

View full text Add to dashboard Cite

In this paper, we find new relations involving the Pell-Padovan sequence which arise as determinants of certain families of Toeplitz-Hessenberg matrices. These determinant formulas may be rewritten as identities involving sums of products of Pell-Padovan numbers and multinomial coefficients. In particular, we establish four connection formulas between the Pell-Padovan and the Fibonacci sequences via Toeplitz-Hessenberg determinants.

show abstract

Section: Toeplitz-hessenberg Determinants and Formulas For Their Evaluationmentioning

confidence: 99%

A note on Pell-Padovan numbers and their connection with Fibonacci numbers

Goy

Sharyn

2020

Carpathian Math. Publ.

View full text Add to dashboard Cite

show abstract

“…with g 1 = −h/2, g 0 = (1 − h 2 /2), and g −n = (h n − h n+2 )/2 for n > 0. Therefore, from the results on the determinant of Toeplitz-Hessenberg matrices [60], by introducing the analytic function…”

Section: Acknowledgementsmentioning

confidence: 99%

Relaxation of the order-parameter statistics in the Ising quantum chain

Collura

2019

SciPost Phys.

View full text Add to dashboard Cite

We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we obtain a full analytical description of the late-time stationary distribution by means of a remarkable relation to the partition function of the 3-states Potts model. Accordingly, depending on the phase whereto the post-quench Hamiltonian belongs, the probability distribution may locally retain memories of the initial long-range order. When quenching deep in the broken-symmetry phase, we proof that the stationary order-parameter statistics is indeed related to that of the ground state. We highlight this connection by inspecting the ground-state equilibrium properties, where we propose an effective description based on the block-diagonal approximation of the n-point spin correlation functions. :1906.00948v1 [cond-mat.stat-mech] Contents arXiv

show abstract

“…From (2) in [14], we thus have the key expansion property expressing the generating function for the determinants as inverse of the original generating function:…”

Section: 2mentioning

confidence: 99%

On extreme events for non-spatial and spatial branching Brownian motions

Avan

Grosjean

Huillet

2015

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

International audienceWe study the impact on shape parameters of an underlying Bienaymé-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then consider spatial branching processes in dimension d, not necessarily integer. The underlying branching mechanism is then either a binary branching model or one presenting infinite variance. In particular we evaluate the chance p(x) of being hit if the epidemics started away at distance x. We compute the large x tail probabilities of this event, both when the branching mechanism is regular and when it exhibits very large fluctuations

show abstract

On determinants of Toeplitz-Hessenberg matrices arising in power series

Cited by 18 publications

References 16 publications

A note on Pell-Padovan numbers and their connection with Fibonacci numbers

A note on Pell-Padovan numbers and their connection with Fibonacci numbers

Relaxation of the order-parameter statistics in the Ising quantum chain

On extreme events for non-spatial and spatial branching Brownian motions

Contact Info

Product

Resources

About