Lower bounds for the $mathcal{A}_{alpha}$-spectral radius of uniform hypergraphs

For $0leq alpha < 1$, the $mathcal{A}_{alpha}$-spectral radius of a $k$-uniform hypergraph $G$ is defined to be the spectral radius of the tensor $mathcal{A}_{alpha}(G):=alpha mathcal{D}(G)+(1-alpha) mathcal{A}(G)$, where $mathcal{D}(G)$ and $A(G)$ are diagonal and the adjacency tensors of $G$ respectively. This paper presents several lower bounds for the difference between the $mathcal{A}_{alpha}$-spectral radius and an average degree $frac{km}{n}$ for a connected $k$-uniform hypergraph with $n$ vertices and $m$ edges, which may be considered as the measures of irregularity of $G$. Moreover, two lower bounds on the $mathcal{A}_{alpha}$-spectral radius are obtained in terms of the maximum and minimum degrees of a hypergraph.