Spectral gap information

In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalues of a matrix or operator; alternately, it is sometimes...

an energy gap is often known more abstractly as a spectral gap, a term which need not be specific to electrons or solids. If an energy gap exists in the...

the graph G is d-regular, there is a relationship between h(G) and the spectral gap d − λ2 of G. An inequality due to Dodziuk and independently Alon and...

ISBN 0-471-55604-1 Spectral gap The Joint spectral radius is a generalization of the spectral radius to sets of matrices. Spectrum of a matrix Spectral abscissa...

is the degree of the vertices of G. The spectral gap of G is defined to be d − λ2, and it measures the spectral expansion of the graph G. If we set λ =...

under perturbation. In spectral clustering, the eigengap is often referred to as the spectral gap; although the spectral gap may often be defined in...

The problem of determining whether a quantum mechanical system has a spectral gap. Finding the capacity of an information-stable finite state machine channel...

later section). In words, convergence is exponential with base being the spectral gap. The power iteration algorithm starts with a vector b 0 {\displaystyle...

as follows: while listening to broadband noise ("white noise") with a spectral gap, if it is switched off a faint tone lasting for several seconds can be...

the gap in the energy eigenvalues (spectral gap) of the Hamiltonian. Specifically, if the system is to be kept in the ground state, the energy gap between...

electron density remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy...

In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal...

_{1}-\lambda _{2}} is called the spectral gap and it is related to the expansion of G. It is also useful to introduce the spectral radius of A {\displaystyle...

S2CID 815023. Hastings, Matthew B.; Koma, Tohru (22 April 2006). "Spectral Gap and Exponential Decay of Correlations". Communications in Mathematical...

Rutgers University. Osting, B. (2012). "Bragg structure and the first spectral gap". Applied Mathematics Letters. 25 (11): 1926–1930. doi:10.1016/j.aml...

2a(n-1)h(M)+10h^{2}(M).} Cheeger constant (graph theory) Isoperimetric problem Spectral gap Cheeger 1971. Buser 1978. Buser 1982. Buser, Peter (1978). "Über eine...

Solves Triple Bubble Problem and More in Quanta magazine. The Role of Convexity in Isoperimetry, Spectral-Gap and Concentration - A Talk by Emanuel Milman...

steps on the graph, where the parameter δ {\displaystyle \delta } is the spectral gap associated to the stochastic matrix P {\displaystyle P} of the graph...

American Mathematical Society. pp. 51–86. ISBN 978-0-8218-9384-5. Ollivier, Yann (2004). "Spectral gap of a graph". Archived from the original on 2007-05-23....

the 0 eigenvalue. The smallest non-zero eigenvalue of L is called the spectral gap. The second smallest eigenvalue of L (could be zero) is the algebraic...

solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states...

use Cheeger's inequality to bound the edge expansion ratio using the spectral gap. Representation theory can be used to construct such expanding Cayley...

in S to the number of vertices in S. 4.  The spectral expansion of a d-regular graph G is the spectral gap between the largest eigenvalue d of its adjacency...