46 citations · 128 across the 37 of their papers we have counts for
5 papers · 1 filter
Quantitative Estimates for Operator-Valued and Infinitesimal Boolean and Monotone Limit Theorems
Octavio Arizmendi, Marwa Banna, Pei-Lun Tseng
We provide Berry-Esseen bounds for sums of operator-valued Boolean and monotone independent variables, in terms of the first moments of the summands. Our bounds are on the level of…
Convergence Rate for The Number of Crossing in a Random Labelled Tree
Santiago Arenas-Velilla, Octavio Arizmendi
We consider the number of crossings in a random labelled tree with vertices in convex position. We give a new proof of the fact that this quantity is asymptotically Gaussian with m…
On the -Schatten Energy of Bipartite Graphs
Octavio Arizmendi, José Guerrero
We give a Coulson integral formula and a Coulson-Jacobs formula for the -Schatten energy. We use this formulas to compare the -Schatten energy of different trees by using a q…
Crossings in Randomly Embedded Graphs
Santiago Arenas-Velilla, Octavio Arizmendi
We consider the number of crossings in a graph which is embedded randomly on a convex set of points. We give an estimate to the normal distribution in Kolmogorov distance which imp…
Cyclic independence: Boolean and monotone
Octavio Arizmendi, Takahiro Hasebe, Franz Lehner
The present paper introduces a modified version of cyclic-monotone independence which originally arose in the context of random matrices, and also introduces its natural analogy ca…