Geodesic
Conjugate Points on a Geodesic with Random Curvature
Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 95-101.

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We study conjugate points on a renewable geodesic on which the curvature is a random process. We construct the upper bound for the mean distance between neighboring conjugate points. 
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V. G. Lamburt. Conjugate Points on a Geodesic with Random Curvature. Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 95-101. http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a6/

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[3] Lamburt V. G., Sokolov D. D., Tutubalin V. N., “Polya Yakobi vdol geodezicheskikh so sluchainoi kriviznoi”, Matem. zametki, 74:3 (2003), 416–424 | MR | Zbl

[4] Lamburt V. G., Rozendorn E. R., Sokolov D. D., Tutubalin V. N., “Geodezicheskie so sluchainoi kriviznoi na rimanovykh i psevdorimanovykh mnogoobraziyakh”, Tr. geometr. seminara Kazanskogo gos. un-ta, 24 (2003), 99–106