arXiv subjects

Ngo P. N. Ngoc

Publications and source records attributed to Ngo P. N. Ngoc.

3 recordsLinked to original sources

arXiv2026

Recurrence and transience of random walks with drift $ρx^α/t^β$

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 $ρx^αt^{-β}$ with $ρ>0$. The case on the critical line $2β-α=1$, with $α\in(-1,1)\setminus\{0\}$, remained open. We prove recurrence in this remaining case. Furthermore, we establish recurrence and transience criteria that complete the classification for $-1<α<1$ and $β\ge 0$, without assuming the Markov property and under weaker assumptions on the increments than those imposed by Menshikov and Volkov.

math.PR↗

arXiv2026

Limit theorems for random walks with spatio-temporal drift

We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models of self-interacting random processes. We determine the asymptotic behavior of the walk under the assumption that its increments have moments of order $p$ for some $p>2$. In the linear case, where the drift depends linearly on the current position, we establish a phase transition in the convergence in distribution of the normalized process to Gaussian limits. In the nonlinear case, we identify three distinct regimes separated by a critical line and show that the normalized process exhibits qualitatively different behaviors in each regime, including convergence in distribution to a Gaussian law, convergence to a non-Gaussian limit given by the stationary distribution of a stochastic differential equation, and almost sure localization on a hypersphere.

math.PR↗

arXiv2025

Open interacting particle systems and Ising measures

We first survey some open questions concerning stochastic interacting particle systems with open boundaries. Then an asymmetric exclusion process with open boundaries that generalizes the lattice gas model of Katz, Lebowitz, and Spohn (KLS) is introduced and invariance of the one-dimensional Ising measure is proved. The stationary current is computed in explicit form and is shown to exhibit current reversal at some density. Based on the extremal-current principle for one-dimensional driven diffusive systems with one conservation law, the phase diagram for boundary-induced phase transitions is conjectured for this case. There are two extremal-current phases, unlike in the conventional open asymmetric simple exclusion process, which exhibits only one extremal-current phase or the previously considered conventional open KLS model with one or three extremal-current phases.

math.PR↗