187 citations · 1.5k across the 105 of their papers we have counts for
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Asymmetric Doob inequalities in continuous time
Guixiang Hong, Marius Junge, Javier Parcet
The present paper is devoted to the second part of our project on asymmetric maximal inequalities, where we consider martingales in continuous time. Let be a nonco…
Subgaussian 1-cocycles on discrete groups
Marius Junge, Qiang Zeng
We prove the Poincaré inequalities with constant for -cocycles on countable discrete groups under Bakry--Emery's -criterion. These inequalities determine…
Noncommutative martingale deviation and Poincaré type inequalities with applications
Marius Junge, Qiang Zeng
We prove a deviation inequality for noncommutative martingales by extending Oliveira's argument for random matrices. By integration we obtain a Burkholder type inequality with sati…
Noncommutative Bennett and Rosenthal inequalities
Marius Junge, Qiang Zeng
In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal i…
The optimal order for the p-th moment of sums of independent random variables with respect to symmetric norms and related combinatorial estimates
Marius Junge
We calculate the p-the moment of the sum of n independent random variables with respect to symmetric norm in R^n. The order of growth for upper bound p/ln p obtained in ths estimat…