On the kernel of tree incidence matrices

نویسندگان

  • M. Bauer
  • O. Golinelli
چکیده

We study the height of the delta peak at 0 in the spectrum of incidence matrices of random trees. We show that the average fraction of the spectrum occupied by the eigenvalue 0 in a large random tree is asymptotic to 2x∗−1 = 0.1342865808195677459999 · · · where x∗ is the unique real root of x = e. For finite trees, we give a closed form, a generating function, and an asymptotic estimate for the sequence (zn)n≥1 = 1, 0, 3, 8, 135, 1164, 21035 · · · of the total multiplicity of the eigenvalue 0 in the set of n tree incidence matrices of size n.

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تاریخ انتشار 2000