Indonesia Combinatorics: [InaCombS] Reminder: Seminar: Random walks, Quantum walks, and Free Meixner Laws

Bapak/Ibu,

Kami mengundang Bapak/Ibu untuk hadir dalam seminar yang akan disampaikan oleh Prof. Nobuaki Obata (Graduate School of Information Sciences, Tohoku University) pada:

Senin, 22 Oktober 2012

Pk. 15.00 – 16.00

Di Ruang Seminar I.2 Prodi Matematika, Labtek III Lantai 1.

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Random walks, Quantum walks, and Free Meixner Laws

Nobuaki Obata

Graduate School of Information Sciences

Tohoku University

In recent years, quantum walks have been studied extensively from various aspects in relation to quantum mechanics and quantum information. The concept of quantum walk was introduced as a quantum mechanical generalization of a random walk, but the correspondence is not straightforward. In this talk I will introduce the so-called Grover walk on a graph, in particular, on a spidernet, and discuss its peculiar property: localization.

A spidernet is a graph obtained from a rooted tree by suitably adding large cycles in each stratum defined by the distance from the root.

The free Meixner distribution appears as the spectral distribution of a spidernet [1], where the quantum probabilistic techniques are applied effectively [2]. It is well known that the spectrum of a graph is related to many properties of random walks. We will see that the spectral analysis is also applied effectively to showing the localization of Grover walks on spidernets [3].

References:

[1] D. Igarashi and N. Obata, Asymptotic spectral analysis of growing graphs: Odd graphs and spidernets, Banach Center Publications 73 (2006), 245-265.

[2] A. Hora and N. Obata, Quantum Probability and Spectral Analysis of Graphs, Springer, 2007.

[3] N. Konno, N. Obata and E. Segawa, Localization of the Grover walks on spidernets and free Meixner laws, arXiv:1206.4422 (June 2012).

Salam,

Dr. Rinovia Simanjuntak

Combinatorial Mathematics Research Group

Faculty of Mathematics and Natural Sciences

Institut Teknologi Bandung

Jl. Ganesa 10 Bandung 40132

Indonesia

Ph. +62-22-250-2545 Ext. 304

Fax. +62-22-250-6450

http://www.math.itb.ac.id/~rino