Growing odd graphs and asymptotic distribution in a
deformed vacuum state
Abstract:
We investigate the asymptotic distribution of odd graphs in a
deformed vacuum state, focusing on the spectral analysis of these
graphs. We explore the adjacency matrices of odd graphs and derive
explicit expressions for their mean and variance in the deformed vacuum
state. Our main results provide the probability measures and the
corresponding coherent states for the distribution of these graphs. We
calculate the Jacobi coefficients and Cauchy transforms related to these
distributions, which have not been addressed explicitly in the existing
literature. Our findings contribute to a deeper understanding of the
probabilistic and spectral properties of odd graphs in quantum state
frameworks.
2010 AMS Mathematics Subject Classification: Primary 46L53;
Secondary 05C50, 60F05.
Keywords and phrases:
adjacency matrix, spectral distribution, quantum decomposition, q-deformed state,
two-sided Rayleigh distribution, odd graph.
