Diederik van Engelenburg

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math.PR2025

One-arm exponents of high-dimensional percolation revisited

Diederik van Engelenburg, Christophe Garban, Romain Panis +1

We consider sufficiently spread-out Bernoulli percolation in dimensions $d > 6$ . We present a short and simple proof of the up-to-constants estimate for the one-arm probability in…

math.PR2025

One-arm exponents of the high-dimensional Ising model

Diederik van Engelenburg, Christophe Garban, Romain Panis +1

We study the probability that the origin is connected to the boundary of the box of size $n$ (the one-arm probability) in several percolation models related to the Ising model. We…

math.PR2020

An upper bound on the two-arms exponent for critical percolation on $Z^{d}$

Jacob van den Berg, Diederik van Engelenburg

Consider critical site percolation on $Z^{d}$ with $d \geq 2$ . Cerf (2015) pointed out that from classical work by Aizenman, Kesten and Newman (1987) and Gandolfi, Grimmett…

One-arm exponents of high-dimensional percolation revisited

One-arm exponents of the high-dimensional Ising model

An upper bound on the two-arms exponent for critical percolation on Zd

An upper bound on the two-arms exponent for critical percolation on $Z^{d}$