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For $0\leq \alpha < 1$, 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 differencebetween 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 areobtained in terms of the maximum and minimum degrees of a hypergraph.

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