Johannes Bäumler

activity

20222026

most citedRecurrence and transience of symmetric random walks with long-range jumps

6 citations · 16 across the 7 of their papers we have counts for

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Showing 2022 · math.PRShow all

4 papers · 2 filters

math.PR2022★ 6 cited

Recurrence and transience of symmetric random walks with long-range jumps

Johannes Bäumler

Let $X_{1}, X_{2}, \dots$ be i.i.d. random variables with values in $Z^{d}$ satisfying $\mathbb{P} \left(X_1=x\right) = \mathbb{P} \left(X_1=-x\right) = Θ\left(\|x\|^{-s}\right…

math.PR2022★ 6 cited

Distances in $\frac{1}{∣ x - y ∣ ^{2 d}}$ percolation models for all dimensions

Johannes Bäumler

We study independent long-range percolation on $Z^{d}$ for all dimensions $d$ , where the vertices $u$ and $v$ are connected with probability 1 for $∥ u - v ∥_{\infty} = 1$ and wit…

math.PR2022★ 2 cited

Behavior of the distance exponent for $\frac{1}{∣ x - y ∣ ^{2 d}}$ long-range percolation

Johannes Bäumler

We study independent long-range percolation on $Z^{d}$ where the vertices $u$ and $v$ are connected with probability asymptotic to $\frac{β}{∥ u - v ∥ ^{2 d}}$ for $\|u-v\|_\infty…

math.PR2022★ 2 cited

Isoperimetric lower bounds for critical exponents for long-range percolation

Johannes Bäumler, Noam Berger

We study independent long-range percolation on $Z^{d}$ where the vertices $x$ and $y$ are connected with probability $1 - e^{- β ∥ x - y ∥^{- d - α}}$ for $α > 0$ . Provided the critic…

Recurrence and transience of symmetric random walks with long-range jumps

Distances in ∣x−y∣2d1​ percolation models for all dimensions

Behavior of the distance exponent for ∣x−y∣2d1​ long-range percolation

Isoperimetric lower bounds for critical exponents for long-range percolation

Distances in $\frac{1}{∣ x - y ∣ ^{2 d}}$ percolation models for all dimensions

Behavior of the distance exponent for $\frac{1}{∣ x - y ∣ ^{2 d}}$ long-range percolation