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Tuan-Minh Nguyen

Monash University

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Preprint Oct 2026

Shape theorem for excited random walks on the integer lattice

We study the limit shape of the range of the random walk excited to the center on $\mathbb Z^d$, with $d\geq2$. A cookie is placed at each nonzero vertex. On its first visit to such a vertex, the walker consumes the cookie and takes its next nearest-neighbor step with a bias toward the origin. On a visit to the origin,...

Tuan-Minh Nguyen · 2 citations

Preprint Sep 2026

Recurrence and transience of random walks with drift $\rho x^{\alpha}/t^{\beta}$

Menshikov and Volkov [Electron. J. Probab. 13 (2008)] studied recurrence and transience of a class of Markovian random walks on $\mathbb R_+$ whose conditional drift depends on both time and position and is of order $\rho x^\alpha t^{-\beta}$ with $\rho>0$. The case on the critical line $2\beta-\alpha=1$, with $\alpha\...

N. P. Ngoc, Tuan-Minh Nguyen · 0 citations

Preprint Aug 2026

Superdiffusivity of random walks on the three-dimensional randomly oriented Manhattan lattice

We study the superdiffusive behavior of random walks on the randomly oriented Manhattan lattice, i.e., the $d$-dimensional integer lattice $\mathbb{Z}^d$ where each axis-aligned line is independently assigned a random direction (forward or backward) with equal probability. The walker takes nearest-neighbor steps, choos...

Tuan-Minh Nguyen · 1 citation · ⚡1