innoschynti, innoschyntinnoschynti, innoschyntinnoschyntinnoschynti
or random walks and percolation on infinite graphs, and
calculating the mathematical limits of
geometric / representational complexity on a plane
This is Los Angeles.
Oh innoskeintis! Thrice have I told your enemies they are involved
in an arms race with a calculator, and thrice they have refused
to sit like dumb babies in a junkyard staring at a bowl
of tea green noodles.
This is a quantum coboobleon...
If
is a continuum percolation in some domain
and f :
! ~
is a conformal map,
then ~ := f( ) (where each loop ` in is mapped conformally to a loop f(`) in ~ ) has
the law of a continuum percolation in ~
. This conformal invariance together with the
above discussion imply that if ! is a scaling limit for (H
; T
), then ~! := f(!) (de ned
by f (Q)(~!) := Q(!) for a dense family of quads Q
) has the law of a continuum
percolation for (H~
; T~
). This type of invariance will be crucial in Section 6.
SECTION 6 (a poem)
Oded Schramm, this is a short (and somewhat informal)
contribution to the proceedings of "The Prong,"
written up by me. I describe how the recent proof of existence
and the conformal covariance of the scaling limits of dynamical
and near-critical planar percolation implies the existence
and several topological properties of the scaling limit
of the Minimal Spanning American Tree, and that it's
co-invariance under Californiño scalings, rotations and
translations represent, or resent perhaps, somewhat, the
non-expectational conformal invariance: I explain why not
and the whatnot is missing not for a proof off course.
There will later "be" proper papers on this subject, after "we"
have finished the proper papers on the scaling limits of
dynamical and near-critical percolation.
Coffee in Los Angeles. Biwa.
Image by Cleon Peterson
