id: 01061872
dt: j
an: 01061872
au: Weineck, Ekkehard
ti: Log-concavity and the spectral gap of stochastic matrices.
so: Comb. Probab. Comput. 6, No.3, 371-379 (1997).
py: 1997
pu: Cambridge University Press, Cambridge
la: EN
cc: 
ut: spectral gap; log-concavity; eigenvalue bound; stochastic matrix
ci: 
li: doi:10.1017/S0963548397002915
ab: Let $Q$ be a stochastic matrix and $I$ the identity matrix. It is shown by
    a direct combinatorial approach that the coefficients of the
    characteristic polynomial of the matrix $I-Q$ are log-concave (a
    sequence $a_0, \dots, a_n$ of real numbers is log-concave if $a^2_i \ge
    a_{i-1} \cdot a_{i+1}$, for all $1\le i\le n-1)$. This fact is used to
    prove a new bound for the second-largest eigenvalue of $Q$, based on
    the subgraphs of an associated graph.
rv: G.Bonanno (Davis)