  In this note we study the spectral form factor in the SYK model in large $q$
limit at infinite temperature. We construct analytic solutions for the saddle
point equations that describe the slope and the ramp regions of the spectral
form factor time dependence. These saddle points are obtained by taking
different approaches to the large $q$ limit: the slope region is described by a
replica-diagonal solution and the ramp region is described by a
replica-nondiagonal solution. We find that the onset of the ramp behavior
happens at the Thouless time of order $q \log q$. We also evaluate the one-loop
corrections to the slope and ramp solutions for late times, and study the
transition from the slope to the ramp. We show this transition is accompanied
by the breakdown of the perturbative $1/q$ expansion, and that the Thouless
time is defined by the consistency of extrapolation of this expansion to late
times.
