# Random walk with random resetting to the maximum position

### Satya N. Majumdar 1 Sanjib Sabhapandit 2 Gregory Schehr 1

#### Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, 92, pp.052126

We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with probability $(1-r)$, it undergoes symmetric random walk, i.e., it hops to one of its neighboring sites, with equal probability $(1-r)/2$. For $r=0$, it reduces to a standard random walk whose typical distance grows as $\sqrt{n}$ for large $n$. In presence of a nonzero resetting rate \$0

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. Raman Research Institute