46 citations · 128 across the 37 of their papers we have counts for
10 papers · 1 filter
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…
Finite Free Cumulants: Multiplicative Convolutions, Genus Expansion and Infinitesimal Distributions
Octavio Arizmendi, Jorge Garza-Vargas, Daniel Perales
Given two polynomials of degree , we give a combinatorial formula for the finite free cumulants of . We show that this formula admits a topolo…
Graphs of Maximal Energy with Fixed Maximal Degree
Octavio Arizmendi, Jorge Fernandez Hidalgo
We give a bound for the graph energy with given maximal degree in terms of the second and fourth moments of a graph. In the case in which the graph is -regular we obtain the bou…
Barabasi-Albert trees are hypoenergetic
Octavio Arizmendi, Emilio Dominguez
We prove that graphs following the model of Barabasi-Albert tree with n vertices are hypoenergetic in the large n limit.
Energy of a graph and Randic index
Gerardo Arizmendi, Octavio Arizmendi
We prove that, for any graph , its graph energy is at least twice the Randic index. We show that equality holds if and only if is the union of complete bipartite graphs.
Energy of a Vertex
Octavio Arizmendi, Jorge Fernandez Hidalgo, Oliver Juarez-Romero
In this paper we develop the concept of energy of a vertex introduced in Arizmendi and Juarez-Romero (2016). We derive basic inequalities, continuity properties, give examples and…
Cumulants for finite free convolution
Octavio Arizmendi, Daniel Perales
In this paper we define cumulants for finite free convolution. We give a moment-cumulant formula and show that these cumulants satisfy desired properties: they are additive with re…
On the spectral distributions of distance-k graph of free product graphs
Octavio Arizmendi, Tulio Gaxiola
We calculate the distribution with respect to the vacuum state of the distance- graph of a -regular tree. From this result we show that the distance- graph of a -regula…
Relations between cumulants in noncommutative probability
Octavio Arizmendi, Takahiro Hasebe, Franz Lehner +1
We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determi…
Statistics of blocks in k-divisible non-crossing partitions
Octavio Arizmendi
We derive a formula for the expected number of blocks of a given size from a non-crossing partition chosen uniformly at random. Moreover, we refine this result subject to the restr…