Maarten Markering

activity

20202026

most citedThe large deviation principle for inhomogeneous Erdős-Rényi random graphs

11 citations · 11 across the 7 of their papers we have counts for

collaborators

7 papers

math.PR2026

The scaling limit of random walk and the intrinsic metric on planar critical percolation

Irina Đanković, Maarten Markering, Jason Miller +1

We consider critical site percolation ( $p = p_{c} = 1/2$ ) on the triangular lattice $T$ in two dimensions. We show that the simple random walk on the clusters of open vertices c…

math.PR2024

Capacity of loop-erased random walk

Maarten Markering

We study the capacity of loop-erased random walk (LERW) on $Z^{d}$ . For $d \geq 4$ , we prove a strong law of large numbers and give explicit expressions for the limit in terms…

math.PR2024

Two-sided infinite self-avoiding walk in high dimensions

Maarten Markering

In this paper, we consider self-avoiding walk (SAW) on $Z^{d}$ for $d \geq 5$ . We construct the \emph{two-sided infinite SAW} and use it to prove pattern theorems for the self…

math.PR2023

Cover times for random walk on dynamical percolation

Maarten Markering

We study the cover time of random walk on dynamical percolation on the torus $Z_{n}^{d}$ in the subcritical regime. In this model, introduced by Peres, Stauffer and Steif, eac…

math.PR2023

Large deviation principle for the norm of the Laplacian matrix of inhomogeneous Erdős-Rényi random graphs

Rajat Subhra Hazra, Frank den Hollander, Maarten Markering

We consider an inhomogeneous Erdős-Rényi random graph $G_{N}$ with vertex set $[N] = {1, \dots, N}$ for which the pair of vertices $i, j \in [N]$ , $i \neq = j$ , is connected by an edge w…

math.PR2021

Breaking of ensemble equivalence for dense random graphs under a single constraint

Frank den Hollander, Maarten Markering

Two ensembles are often used to model random graphs subject to constraints: the microcanonical ensemble (= hard constraint) and the canonical ensemble (= soft constraint). It is sa…

math.PR2020★ 11 cited

The large deviation principle for inhomogeneous Erdős-Rényi random graphs

Maarten Markering

Consider the inhomogeneous Erdős-Rényi random graph (ERRG) on $n$ vertices for which each pair $i, j \in {1, \dots, n}$ , $i \neq = j$ is connected independently by an edge with probabil…