Limit theorems for the trajectory of the self-repelling random walk with directed edges
L Marêché, T Mountford - Electronic Journal of Probability, 2024 - projecteuclid.org
The self-repelling random walk with directed edges was introduced by Tóth and Vető in
2008 [23] as a nearest-neighbor random walk on ℤ that is non-Markovian: at each step, the …
2008 [23] as a nearest-neighbor random walk on ℤ that is non-Markovian: at each step, the …
Convergence and nonconvergence of scaled self-interacting random walks to Brownian motion perturbed at extrema
E Kosygina, T Mountford, J Peterson - The Annals of Probability, 2023 - projecteuclid.org
We use generalized Ray–Knight theorems, introduced by B. Tóth in 1996, together with
techniques developed for excited random walks as main tools for establishing positive and …
techniques developed for excited random walks as main tools for establishing positive and …
Fluctuations of the local times of the self-repelling random walk with directed edges
L Marêché - Advances in Applied Probability, 2024 - cambridge.org
In 2008, Tóth and Vető defined the self-repelling random walk with directed edges as a non-
Markovian random walk on topology, as well as in the uniform topology away from the …
Markovian random walk on topology, as well as in the uniform topology away from the …
A Functional Central Limit Theorem for the General Brownian Motion on the Half-Line
In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the
convergence in distribution of Feller processes by examining the convergence of their …
convergence in distribution of Feller processes by examining the convergence of their …
Scaling Limit of Asymptotically-free Self-interacting Random Walks to Brownian Motion Perturbed at Extrema
X Liu, Z Wang - arXiv preprint arXiv:2402.11828, 2024 - arxiv.org
We show convergence of a family of one-dimensional self-interacting random walks to
Brownian motion perturbed at extrema under the diffusive scaling. This completes the …
Brownian motion perturbed at extrema under the diffusive scaling. This completes the …
Speed of excited random walks with long backward steps
TM Nguyen - Journal of Statistical Physics, 2022 - Springer
We study a model of multi-excited random walk with non-nearest neighbour steps on Z, in
which the walk can jump from a vertex x to either x+ 1 or xi with i∈{1, 2,⋯, L}, L≥ 1. We first …
which the walk can jump from a vertex x to either x+ 1 or xi with i∈{1, 2,⋯, L}, L≥ 1. We first …
Waiting Times for Ties in Random Competitions
I Matic - arXiv preprint arXiv:2105.01310, 2021 - arxiv.org
Multiple teams participate in a random competition. In each round the winner receives one
point. We study the times until ties occur among teams. We construct martingales and …
point. We study the times until ties occur among teams. We construct martingales and …