# Random walk on p-adics and hierarchical systems

## Abstract

We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical systems. For our purposes, we specify the Markov stochastic process considered by Albeverio and Karwowski. As a result we have obtained a random walk on the p-adic integer numbers, which provides the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.

- Authors:

- Institute of Physics, University of Zielona Gora, ul. Z. Szafrana 4a, 65-516 Zielona Gora (Poland)
- (Poland)

- Publication Date:

- OSTI Identifier:
- 20787909

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevB.73.054419; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; DECAY; LATTICE FIELD THEORY; MARKOV PROCESS; RANDOMNESS; RELAXATION; TEMPERATURE DEPENDENCE

### Citation Formats

```
Lukierska-Walasek, K., Topolski, K., and Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw.
```*Random walk on p-adics and hierarchical systems*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVB.73.0.

```
Lukierska-Walasek, K., Topolski, K., & Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw.
```*Random walk on p-adics and hierarchical systems*. United States. doi:10.1103/PHYSREVB.73.0.

```
Lukierska-Walasek, K., Topolski, K., and Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw. Wed .
"Random walk on p-adics and hierarchical systems". United States.
doi:10.1103/PHYSREVB.73.0.
```

```
@article{osti_20787909,
```

title = {Random walk on p-adics and hierarchical systems},

author = {Lukierska-Walasek, K. and Topolski, K. and Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw},

abstractNote = {We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical systems. For our purposes, we specify the Markov stochastic process considered by Albeverio and Karwowski. As a result we have obtained a random walk on the p-adic integer numbers, which provides the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.},

doi = {10.1103/PHYSREVB.73.0},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 5,

volume = 73,

place = {United States},

year = {Wed Feb 01 00:00:00 EST 2006},

month = {Wed Feb 01 00:00:00 EST 2006}

}

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