The Sided Restriction Measure And Estimate Of Related Probability For SLE

Chrodal left-sided restriction measure is defined, and its equivalence is characterized.The chrodal left-sided restriction measure is constructed by the approach of re?ected Brown-ian motion. The relationship between the one-sided restriction measure and two-sided restric-tion measure is obtained.The probability formula for a chordal S LEκ(0≤κ< 8) trace across a given point inupper half plane H is derived. The probability formula for a critical percolation in a closedunit disk which doesn't contain a fixed point is established. It is proved that the trace of S LE6and self-avoiding walk with the same start point and end one have identical distribution.On the basis of the probability that a chordal S LEκpath in the upper half plane H inter-sects a semicircle on the real line , we derive the probability that a chordal S LEκpath in theupper half plane intersects a circle in the upper half plane H. And we get the probability thata chordal S LEκpath in the upper half plane intersects a rectangle in the upper half plane H.The related probability of local martingale is obtained and we establish the estimate ofthe hitting probability of a S LEκ(4 <κ< 8) with three small intervals on the real line.