Abstract: In this talk, we first introduce the countable matrix and graph, the irreducibility and aperiodicity of the countable matrix, and the corresponding Perron eigenvalue and the Gurevich entropy. Also, we introduce the Vere-Jones classification which provides a criterion to determine whether the countable matrix is transient, null recurrent, weakly positive recurrent or strongly positive recurrent. Moreover, we introduce an invariant Borel probability measure on the countable graph, which is related to the Gurevich entropy. Finally, we introduce the rome of a graph and the rome matrix, which enable us to obtain the characteristic polynomial of the transition matrix of the graph and compute the eigenvalues in a more convenient way.

 

Organizer: Jung-Chao Ban (NCCU)