Random walks and the effective resistance sum rules

A graph may be regarded as an electrical network in which each edge has unit resistance. We obtain explicit formulae for the effective resistance of the network when a current enters at one vertex and leaves at another in the distance-regular case. A well-known link with random walks motivates a conjecture about the maximum effective resistance. Arguments are given that point to the truth of the conjecture for all known distance-regular graphs.

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Random walks and the effective resistance of networks

Journal of Theoretical Probability ◽

10.1007/bf01046996 ◽

1991 ◽

Vol 4 (1) ◽

pp. 101-109 ◽

Cited By ~ 179

Author(s):

Prasad Tetali

Keyword(s):

Random Walks ◽

Effective Resistance

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TWO-POINT RESISTANCES IN SAILBOAT FRACTAL NETWORKS

Fractals ◽

10.1142/s0218348x20500279 ◽

2020 ◽

Vol 28 (02) ◽

pp. 2050027

Author(s):

JIALI ZHU ◽

LI TIAN ◽

JIAQI FAN ◽

LIFENG XI

Keyword(s):

Sum Rules ◽

Recursive Algorithm ◽

Effective Resistance ◽

Substitution Principle ◽

Self Similar ◽

Fractal Network

The two-point resistance of fractal network has been studied extensively by mathematicians and physicists. In this paper, for a class of self-similar networks named sailboat networks, we obtain a recursive algorithm for computing resistance between any two nodes, using elimination principle, substitution principle and local sum rules on effective resistance.

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A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

International Astronomical Union Colloquium ◽

10.1017/s025292110010805x ◽

1988 ◽

Vol 102 ◽

pp. 343-347

Author(s):

M. Klapisch

Keyword(s):

Perturbation Theory ◽

Small Parameter ◽

Classification Scheme ◽

Sum Rules ◽

Energy Levels ◽

Natural Classification ◽

Quantum Numbers ◽

Formal Expansion ◽

Atomic Energy Levels ◽

As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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