Asymptotic Spectral Analysis of Growing Graphs: A Quantum Probabilistic Approach
نویسنده
چکیده
We review the recently developed method for spectral analysis of growing graphs on the basis of quantum (or noncommutative or algebraic) probability theory. The asymptotic spectral distribution of a growing regular graph is derived from the quantum central limit theorem for quantum components of the adjacency matrix. Mathematics Subject Classifications (2000): Primary 46L53; Secondary 05C50, 42C05, 60F05, 81S25.
منابع مشابه
The reliability Wiener number of cartesian product graphs
Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...
متن کاملInvestigation of Continuous-Time Quantum Walk Via Spectral Distribution Associated with Adjacency Matrix
Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph Cn, complete graph Kn, graph Gn, finite path and some other finite and infinite graphs, where all are connected with orthogonal polynomials such as Hermite, Laguerre, Tche...
متن کاملSpectral asymptotics of percolation Hamiltoni- ans on amenable Cayley graphs
In this paper we study spectral properties of adjacency and Laplace operators on percolation subgraphs of Cayley graphs of amenable, finitely generated groups. In particular we describe the asymptotic behaviour of the integrated density of states (spectral distribution function) of these random Hamiltonians near the spectral minimum. The first part of the note discusses various aspects of the q...
متن کاملThe Use of Monte-Carlo Simulations in Seismic Hazard Analysis in Tehran and Surrounding Areas
Probabilistic seismic hazard analysis is a technique for estimating the annual rate of exceedance of a specified ground motion at a site due to the known and suspected earthquake sources. A Monte-Carlo approach is utilized to estimate the seismic hazard at a site. This method uses numerous resampling of an earthquake catalog to construct synthetic catalogs to evaluate the ground motion hazard a...
متن کاملQuantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to the spectral theory of quantum graphs and discuss exact trace formulae for the spectrum and the quantum-to-classical correspondence. The second part of this ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013