English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a continuous-time branching random walk on $\mathbb{Z}$ in arandom non homogeneous environment. Particles can walk on the lattice points ordisappear with random intensities. The process starts with one particle atinitial time $t=0$. It can walk on the lattice points or disappear with arandom intensity until it reach the point, where initial particle can splitinto two offspring. This lattice point we call reproduction source. Theoffspring of the initial particle evolve according to the same law,independently of each other and the entire prehistory. The aim of the paper isto study the conditions for the presence of exponential growth of the averagenumber of particle at an every lattice point. For this purpose we investigatethe spectrum of the random evolution operator of the average particle numbers.We derive the condition under which there is exponential growth withprobability one. We also study the process under the violation of thiscondition and present the lower and upper estimates for the probability ofexponential growth.

Branching Random Walks in a Random Killing Environment with a Single Reproduction Source