5 research outputs found
Which Graphs are Determined by their Spectrum?
AMS classifications; 05C50; 05E30;
Inverse problems for discrete heat equations and random walks
We study the inverse problem of determining a finite weighted graph
from the source-to-solution map on a vertex subset for heat
equations on graphs, where the time variable can be either discrete or
continuous. We prove that this problem is equivalent to the discrete version of
the inverse interior spectral problem, provided that there does not exist a
nonzero eigenfunction of the weighted graph Laplacian vanishing identically on
. In particular, we consider inverse problems for discrete-time random walks
on finite graphs. We show that under the Two-Points Condition, the graph
structure and the transition matrix of the random walk can be uniquely
recovered from the distributions of the first passing times on , or from the
observation on of one realization of the random walk.Comment: 31 pages, 3 figures. arXiv admin note: text overlap with
arXiv:2101.1002