  We examine the equilibrium fluctuation spectrum of a constituent semiflexible
filament segment in a network. The effect of this cross linking is to modify
the mechanical boundary conditions at the end of the filament. We consider the
effect of both tensile stress in the network, and its elastic compliance. Most
significantly, the network's compliance introduces a nonlinear term into the
filament Hamiltonian even in the small-bending approximation. We analyze the
effect of this nonlinearity upon the filament's fluctuation profile. We also
find that there are three principal fluctuation regimes dominated by one of the
following: (i) network tension, (ii) filament bending stiffness, or (iii)
network compliance. We propose that one can use observed filament fluctuations
as a noninvasive probe of network tension, and we provide the necessary
response function to quantitatively analyze this sort of "tension
microrheology" in cross linked semiflexible filament networks.
