Geodesic
Measure comparison problems for dilations of convex bodies
Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 270-285

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DOI

We study a version of the Busemann-Petty problem for $\log $-concave measures with an additional assumption on the dilates of convex, symmetric bodies. One of our main tools is an analog of the classical large deviation principle applied to $\log $-concave measures, depending on the norm of a convex body. We hope this will be of independent interest.
DOI : 10.4153/S0008439524000729
Mots-clés : Busemann-Petty problem, log-concavity, large deviation 
Lafi, Malak; Zvavitch, Artem. Measure comparison problems for dilations of convex bodies. Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 270-285. doi: 10.4153/S0008439524000729
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     title = {Measure comparison problems for dilations of convex bodies},
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     pages = {270--285},
     year = {2025},
     volume = {68},
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     doi = {10.4153/S0008439524000729},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000729/}
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