Debbasch, F. A diffusion process in curved space-time. (English) Zbl 1071.82031 J. Math. Phys. 45, No. 7, 2744-2760 (2004). Summary: We construct a curved space–time generalization of the special relativistic Ornstein–Uhlenbeck Process. This is done by deriving a manifestly covariant Kolmogorov equation that describes diffusion in curved space–times. The simple case of diffusion in a spatially flat Friedmann–Robertson–Walker universe is then considered. It is proven that, at least in these space–times, Kolmogorov equation admits as possible solution a natural generalization of the flat space–time Jüttner equilibrium solution. The first correction to Jüttner’s distribution in a slowly expanding universe is also obtained explicitly. Cited in 17 Documents MSC: 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 83C47 Methods of quantum field theory in general relativity and gravitational theory PDFBibTeX XMLCite \textit{F. Debbasch}, J. Math. Phys. 45, No. 7, 2744--2760 (2004; Zbl 1071.82031) Full Text: DOI References: [1] Debbasch F., J. Stat. Phys. 88 pp 945– (1997) · Zbl 0939.82015 · doi:10.1023/B:JOSS.0000015180.16261.53 [2] Debbasch F., J. Stat. Phys. 90 pp 1179– (1998) · Zbl 0920.60091 · doi:10.1023/A:1023275210656 [3] Barbachoux C., Eur. Phys. J. B 19 pp 37– (2001) · Zbl 1230.82044 · doi:10.1007/s100510170348 [4] Barbachoux C., Eur. Phys. J. B 23 pp 487– (2001) · Zbl 1230.82040 · doi:10.1140/e10051-001-0002-6 [5] Titulaer U. M., Z. Phys. B 50 pp 71– (1978) · doi:10.1007/BF01307229 [6] DOI: 10.1007/BF01340339 · doi:10.1007/BF01340339 [7] Barbachoux C., J. Math. Phys. 40 pp 2891– (1999) · Zbl 0973.82040 · doi:10.1063/1.532734 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.