# Dense-dilute factorization for a class of stochastic processes and for high energy QCD

## Abstract

Stochastic processes described by evolution equations in the universality class of the Fisher-Kolmogorov-Petrovsky-Piscounov equation may be approximately factorized into a linear stochastic part and a nonlinear deterministic part. We prove this factorization on a model with no spatial dimensions and we illustrate it numerically on a one-dimensional toy model that possesses some of the main features of high energy QCD evolution. We explain how this procedure may be applied to QCD amplitudes, by combining Salam's Monte Carlo implementation of the dipole model and a numerical solution of the Balitsky-Kovchegov equation.

- Authors:

- Centre de Physique Theorique, Ecole Polytechnique, CNRS, 91128 Palaiseau (France)

- Publication Date:

- OSTI Identifier:
- 21010985

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevD.75.034009; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; DIPOLES; FACTORIZATION; FIELD EQUATIONS; MONTE CARLO METHOD; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; ONE-DIMENSIONAL CALCULATIONS; QUANTUM CHROMODYNAMICS; STOCHASTIC PROCESSES

### Citation Formats

```
Munier, Stephane.
```*Dense-dilute factorization for a class of stochastic processes and for high energy QCD*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.034009.

```
Munier, Stephane.
```*Dense-dilute factorization for a class of stochastic processes and for high energy QCD*. United States. doi:10.1103/PHYSREVD.75.034009.

```
Munier, Stephane. Thu .
"Dense-dilute factorization for a class of stochastic processes and for high energy QCD". United States.
doi:10.1103/PHYSREVD.75.034009.
```

```
@article{osti_21010985,
```

title = {Dense-dilute factorization for a class of stochastic processes and for high energy QCD},

author = {Munier, Stephane},

abstractNote = {Stochastic processes described by evolution equations in the universality class of the Fisher-Kolmogorov-Petrovsky-Piscounov equation may be approximately factorized into a linear stochastic part and a nonlinear deterministic part. We prove this factorization on a model with no spatial dimensions and we illustrate it numerically on a one-dimensional toy model that possesses some of the main features of high energy QCD evolution. We explain how this procedure may be applied to QCD amplitudes, by combining Salam's Monte Carlo implementation of the dipole model and a numerical solution of the Balitsky-Kovchegov equation.},

doi = {10.1103/PHYSREVD.75.034009},

journal = {Physical Review. D, Particles Fields},

number = 3,

volume = 75,

place = {United States},

year = {Thu Feb 01 00:00:00 EST 2007},

month = {Thu Feb 01 00:00:00 EST 2007}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.