A~one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 56 (2001) no. 4, pp. 687-708
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The surprising connection between a one-dimensional gravitationally interacting gas of sticky
particles and the convex minorant process generated by Brownian motion on $[0,1]$ is studied. A study is made of the dynamics of this 1-D gas system by identifying three distinct clustering regimes and the time scales at which they occur. At the critical moment of time the mass distribution of the gas can be computed in terms of functionals of the convex minorant process.
@article{RM_2001_56_4_a2,
author = {T. M. Suidan},
title = {A~one-dimensional gravitationally interacting gas and the convex minorant of {Brownian} motion},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {687--708},
publisher = {mathdoc},
volume = {56},
number = {4},
year = {2001},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_2001_56_4_a2/}
}
TY - JOUR AU - T. M. Suidan TI - A~one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 2001 SP - 687 EP - 708 VL - 56 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/RM_2001_56_4_a2/ LA - en ID - RM_2001_56_4_a2 ER -
%0 Journal Article %A T. M. Suidan %T A~one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 2001 %P 687-708 %V 56 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/RM_2001_56_4_a2/ %G en %F RM_2001_56_4_a2
T. M. Suidan. A~one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 56 (2001) no. 4, pp. 687-708. http://geodesic.mathdoc.fr/item/RM_2001_56_4_a2/