22 citations · 22 across the 3 of their papers we have counts for
8 papers
Every decision tree has an influential variable
Ryan O'Donnell, Michael Saks, Oded Schramm +1
We prove that for any decision tree calculating a boolean function , \[ \Var[f] \le \sum_{i=1}^n δ_i \Inf_i(f), \] where is the probability that the…
Pinched exponential volume growth implies an infinite dimensional isoperimetric inequality
Itai Benjamini, Oded Schramm
Let be a graph which satisfies , for some constants , every vertex and every radius . We prove that this implies the isoperimet…
A negative answer to Nevanlinna's type question and a parabolic surface with a lot of negative curvature
Itai Benjamini, Sergei Merenkov, Oded Schramm
Consider a simply connected Riemann surface represented by a Speiser graph. Nevanlinna asked if the type of the surface is determined by the mean excess of the graph: whether mean…
On the scaling limit of planar self-avoiding walk
Gregory F. Lawler, Oded Schramm, Wendelin Werner
A planar self-avoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no self-intersection. A planar self-avoiding polygon (SAP) is a loop with no sel…
One-arm exponent for critical 2D percolation
Gregory F. Lawler, Oded Schramm, Wendelin Werner
The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than is proved to decay like as .
A percolation formula
Oded Schramm
Let be an arc on the boundary of the unit disk . We prove an asymptotic formula for the probability that there is a percolation cluster for critical site percolation on…