On one top news list model

We introduce a top news list model based on extremal shot noise with Poisson arrival flow. We find one- and multi-dimensional distributions of popularity of current news (at arbitrary time and at infinity), as well as distributions of places of news in a top list and their sojourn times in a stationary regime. We consider in detail the case where the popularity of a news item is Pareto distributed at the initial time and then decreases exponentially.