# gst: apropos of survival, diffusion with stochastic resetting in the presence of a delta killing trap; drift-controlled survival regimes.

<< ️(AA) study a one-dimensional diffusive particle subject to stochastic resetting to its initial position, in the presence of an imperfect, localized target that can absorb (kill) the particle, modeled by a delta-function killing rate. >>

<< ️The central question is how stochastic resetting competes with drift-induced transience and the target's finite reactivity. >>

 

<< ️The long-time behavior separates into distinct regimes. Without resetting, unbiased diffusion exhibits the recurrent algebraic survival law 𝑆⁡(𝑡)∼𝑡−1/2, whereas any nonzero drift renders the motion transient with respect to the target and leaves a nonzero ultimate survival probability. >>

<< ️By contrast, any 𝑟>0 and 𝑘>0 repeatedly renew encounters with the target and restore eventual absorption, yielding an exponential survival law 𝑆⁡(𝑡)∼𝐴⁢𝑒−𝜃⁢𝑡. The decay rate 𝜃 is given by the dominant (rightmost) pole of the Laplace transform, and the surviving density converges after normalization to an explicit quasistationary profile. The driftless and perfectly absorbing limits recover standard resetting results. >>

<< ️These (AA) formulas provide a unified description of the crossover between recurrence-controlled, transience-controlled, and renewal-controlled survival. >>

A. Mazzolo. Diffusion with stochastic resetting in the presence of a delta killing trap: Drift-controlled survival regimes. Phys. Rev. E 114, 044105. Oct 5, 2026.

https://journals.aps.org/pre/abstract/10.1103/3s1c-k5vg

arXiv: 2609.22527v1 [cond-mat.stat-mech]. Sep 18, 2026.

https://arxiv.org/abs/2609.22527

Also: particle, behav, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, behavior, transitions, stochasticity, stochastic processes, stochastic resetting, drift-induced transience, target finite reactivity, survival probability, long-time behavior, unbiased diffusion, absorption, decay rate, recurrence-controlled survival, transience-controlled survival, renewal-controlled survival, brownian motion, diffusion.