@article{FruehwirthProchno2023, author = {Fr{\"u}hwirth, Lorenz and Prochno, Joscha}, title = {H{\"o}lder's inequality and its reverse — a probabilistic point of view}, series = {Mathematische Nachrichten}, volume = {296}, journal = {Mathematische Nachrichten}, number = {12}, publisher = {Wiley}, address = {Hoboken}, doi = {10.1002/mana.202200411}, url = {http://nbn-resolving.de/urn:nbn:de:101:1-2023062315175042989607}, pages = {5493 -- 5512}, year = {2023}, abstract = {In this article, we take a probabilistic look at H{\"o}lder's inequality, considering the ratio of terms in the classical H{\"o}lder inequality for random vectors in ℝ𝑛. We prove a central limit theorem for this ratio, which then allows us to reverse the inequality up to a multiplicative constant with high probability. The models of randomness include the uniform distribution on 𝓁𝑛𝑝 balls and spheres. We also provide a Berry-Esseen-type result and prove a large and a moderate deviation principle for the suitably normalized H{\"o}lder ratio.}, language = {en} }