Current Trends in Random Walks on Random Lattices

In a classical random walk model, walker moves through deterministic d-dimensional integer lattice in one step at time, without drifting any direction. more advanced setting, randomly over configured (non equidistant) jumping number of steps. some further variants, there is limited access walker’s moves. That is, the movements are not available real time. Instead, observations to epochs resulting delayed information about real-time position walker, its escape and location outside bounded subset space. this case we target virtual first passage (or escape) Thus, unlike standard problems, rather than crossing boundary, deal with arbitrarily distant from boundary. paper, give short historical background on walk, discuss various directions development theory, survey most our results obtained last 25–30 years, including very recent ones dated 2020–21. Among different applications such walks, stock markets, stochastic networks, games, queueing.