# Random functions via Dyson Brownian Motion: progress and problems

## Abstract

We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C{sup 2} locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.

- Authors:

- Institute for Astrophysics, University of Goettingen,Friedrich Hund Platz 1, D-37077 Goettingen (Germany)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22572144

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2016; Journal Issue: 09; Other Information: PUBLISHER-ID: JCAP09(2016)008; OAI: oai:repo.scoap3.org:17039; cc-by Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AXIONS; BROWNIAN MOVEMENT; COSMOLOGICAL INFLATION; COSMOLOGY; DYSON REPRESENTATION; INFLATIONARY UNIVERSE; RANDOMNESS; STRING THEORY

### Citation Formats

```
Wang, Gaoyuan, and Battefeld, Thorsten.
```*Random functions via Dyson Brownian Motion: progress and problems*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/09/008.

```
Wang, Gaoyuan, & Battefeld, Thorsten.
```*Random functions via Dyson Brownian Motion: progress and problems*. United States. doi:10.1088/1475-7516/2016/09/008.

```
Wang, Gaoyuan, and Battefeld, Thorsten. Mon .
"Random functions via Dyson Brownian Motion: progress and problems". United States.
doi:10.1088/1475-7516/2016/09/008.
```

```
@article{osti_22572144,
```

title = {Random functions via Dyson Brownian Motion: progress and problems},

author = {Wang, Gaoyuan and Battefeld, Thorsten},

abstractNote = {We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C{sup 2} locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.},

doi = {10.1088/1475-7516/2016/09/008},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2016,

place = {United States},

year = {Mon Sep 05 00:00:00 EDT 2016},

month = {Mon Sep 05 00:00:00 EDT 2016}

}

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