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no. 5
The distance problem on measured metric spaces
David Aldous1 ; Guillaume Blanc2 ; Nicolas Curien3
1 Department of Statistics, 367 Evans Hall # 3860, U.C. Berkeley, CA 94720, USA
2 EPFL, MA A2 397, (Bâtiment MA) Station 8 1015 Lausanne, Switzerland
3 Université Paris-Saclay, BP74, 38402 SMH Cedex, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 34 (2025) no. 5, pp. 1345-1365

What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture that every distribution with a density function whose support contains $0$ does arise in this way, and give some partial results in that direction.

Quelles distributions apparaissent comme lois de la distance entre deux points typiques dans un espace métrique mesuré ? Cette question naturelle semble étonnamment subtile. Nous conjecturons que toute distribution possédant une densité dont le support contient 0 peut apparaître de cette maniere. Nous étayons cette conjecture par des résultats partiels.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1835
Classification : 60B05, 60E99
Keywords: Characterization of distribution, construction of distribution, distance, measured metric space, tree
Mots-clés : caractérisation de loi, distance, espace métrique mesuré, arbre

David Aldous 1 ; Guillaume Blanc 2 ; Nicolas Curien 3

1 Department of Statistics, 367 Evans Hall # 3860, U.C. Berkeley, CA 94720, USA
2 EPFL, MA A2 397, (Bâtiment MA) Station 8 1015 Lausanne, Switzerland
3 Université Paris-Saclay, BP74, 38402 SMH Cedex, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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David Aldous; Guillaume Blanc; Nicolas Curien. The distance problem on measured metric spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 34 (2025) no. 5, pp. 1345-1365. doi: 10.5802/afst.1835

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