  We investigate slow-roll inflation in a multi-field random Gaussian
landscape. The landscape is assumed to be small-field, with a correlation
length much smaller than the Planck scale. Inflation then typically occurs in
small patches of the landscape, localized near inflection or saddle points. We
find that the inflationary track is typically close to a straight line in the
field space, and the statistical properties of inflation are similar to those
in a one-dimensional landscape. This picture of multi-field inflation is rather
different from that suggested by the Dyson Brownian motion model; we discuss
the reasons for this difference. We also discuss tunneling from inflating false
vacua to the neighborhood of inflection and saddle points and show that the
tunneling endpoints tend to concentrate along the flat direction in the
landscape.
