The spectrum of a local random Hamiltonian can be represented generically by the so-called ε-free convolution of its local terms’ probability distributions. For the purpose of studying its spectrum, we establish an isomorphism between the set of ε-noncrossing partitions and permutations. Moreover, we derive some lower and upper bounds for the maximal eigenvalue of the Hamiltonian.

This talk is based on joint works with Benoit Collins (Kyoto), Liang Zhao (Harbin), and   Ping Zhong (Wyoming).

会议密码:2022