PreprintCC0arXiv
Stability of the Markov-Krein Transform Under Classical Convolutions
Abstract
We prove that, for every c>0, the image of the generalized Markov-Krein transform on probability measures with finite logarithmic moment is closed under classical additive convolution and under the Mellin convolution. This resolves the positivity conjecture for the additive high-temperature convolution, a one-parameter interpolation between classical and free convolution arising in random matrix theory and representation theory in the regime N→∞, NβN/2→ c. Our proof relies on a convolution theorem for universally prestarlike functions.
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BibTeX
@misc{mergny2026stability,
title = {{Stability of the Markov-Krein Transform Under Classical Convolutions}},
author = {Pierre Mergny},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18436},
eprint = {2610.18436},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18436},
note = {CC0},
}
RIS
TY - UNPB
TI - Stability of the Markov-Krein Transform Under Classical Convolutions
AU - Pierre Mergny
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18436
UR - https://arxiv.org/abs/2610.18436
AB - We prove that, for every c>0, the image of the generalized Markov-Krein transform on probability measures with finite logarithmic moment is closed under classical additive convolution and under the Mellin convolution. This resolves the positivity conjecture for the additive high-temperature convolution, a one-parameter interpolation between classical and free convolution arising in random matrix theory and representation theory in the regime N→∞, Nβ_N/2→ c. Our proof relies on a convolution theorem for universally prestarlike functions.
ER -