scholarly journals ASYMPTOTIC BEHAVIOR OF THE INTEGRATED DENSITY OF STATES FOR RANDOM POINT FIELDS ASSOCIATED WITH CERTAIN FREDHOLM DETERMINANTS

2019 ◽  
Vol 73 (1) ◽  
pp. 43-67
Author(s):  
Naomasa UEKI
Keyword(s):  
Asymptotic Behavior ◽  
Density Of States ◽  
Random Point ◽  
Integrated Density Of States ◽  
Fredholm Determinants

scholarly journals Asymptotics of Negative Exponential Moments for Annealed Brownian Motion in a Renormalized Poisson Potential

2011 ◽  
Vol 2011 ◽  
pp. 1-43 ◽  
Author(s):  
Xia Chen ◽  
Alexey Kulik
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Detailed Analysis ◽  
Density Of States ◽  
Random Schrödinger Operators ◽  
Integrated Density Of States ◽  
Random Potentials ◽  
Lifshitz Tails ◽  
Exponential Moments ◽  
Negative Exponential

In (Chen and Kulik, 2009), a method of renormalization was proposed for constructing some more physically realistic random potentials in a Poisson cloud. This paper is devoted to the detailed analysis of the asymptotic behavior of the annealed negative exponential moments for the Brownian motion in a renormalized Poisson potential. The main results of the paper are applied to studying the Lifshitz tails asymptotics of the integrated density of states for random Schrödinger operators with their potential terms represented by renormalized Poisson potentials.

scholarly journals Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

2020 ◽  
pp. 1-14
Author(s):  
SHOTA OSADA
Keyword(s):  
Point Processes ◽  
Duke Math ◽  
Random Point ◽  
Determinantal Point Processes ◽  
Fredholm Determinants ◽  
Poisson Point Processes ◽  
Translation Invariant ◽  
Ergodic Properties ◽  
Tree Representations ◽  
Invariant Kernels

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

scholarly journals The landscape law for the integrated density of states

2021 ◽  
Vol 390 ◽  
pp. 107946
Author(s):  
G. David ◽  
M. Filoche ◽  
S. Mayboroda
Keyword(s):  
Density Of States ◽  
Integrated Density Of States

GAP-LABELING PROPERTIES OF THE ENERGY SPECTRUM FOR TWO-DIMENSIONAL FIBONACCI QUASILATTICES

1995 ◽  
Vol 09 (01) ◽  
pp. 55-66
Author(s):  
YOUYAN LIU ◽  
WICHIT SRITRAKOOL ◽  
XIUJUN FU
Keyword(s):  
Energy Spectrum ◽  
Density Of States ◽  
Energy Gap ◽  
Fractional Part ◽  
Numerical Results ◽  
Step Height ◽  
Integrated Density Of States ◽  
Two Dimensional

We have analytically obtained the occupation probabilities on subbands of the hierarchical energy spectrum and the step heights of the integrated density of states for two-dimensional Fibonacci quasilattices. Based on the above results, the gap-labeling properties of the energy spectrum are found, which claim that the step height is equal to {mτ}, where the braces denote the fractional part, and m is an integer that can be used to label the corresponding energy gap. Numerical results confirm these results very well.

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