Filters

2020 - 20216

More filters

20226
Reset filters

Settings

End date: 2024 × Start date: 2020 × DDC: 510 × Publisher: [Madralin] : EMIS ELibEMS ×

Search Results

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    Poisson approximation and connectivity in a scale-free random connection model
    ([Madralin] : EMIS ELibEMS, 2021) Iyer, Srikanth K.; Jhawar, Sanjoy Kr
    For abstract see PDF
  • Thumbnail Image
    Item
    Phase transitions for chase-escape models on Poisson–Gilbert graphs
    ([Madralin] : EMIS ELibEMS, 2020) Hinsen, Alexander; Jahnel, Benedikt; Cali, Elie; Wary, Jean-Philippe
    We present results on phase transitions of local and global survival in a two-species model on Poisson–Gilbert graphs. Initially, there is an infection at the origin that propagates on the graph according to a continuous-time nearest-neighbor interacting particle system. The graph consists of susceptible nodes and nodes of a second type, which we call white knights. The infection can spread on susceptible nodes without restriction. If the infection reaches a white knight, this white knight starts to spread on the set of infected nodes according to the same mechanism, with a potentially different rate, giving rise to a competition of chase and escape. We show well-definedness of the model, isolate regimes of global survival and extinction of the infection and present estimates on local survival. The proofs rest on comparisons to the process on trees, percolation arguments and finite-degree approximations of the underlying random graphs.
  • Thumbnail Image
    Item
    Rough invariance principle for delayed regenerative processes
    ([Madralin] : EMIS ELibEMS, 2021) Orenshtein, Tal
    We derive an invariance principle for the lift to the rough path topology of stochastic processes with delayed regenerative increments under an optimal moment condition. An interesting feature of the result is the emergence of area anomaly, a correction term in the second level of the limiting rough path which is identified as the average stochastic area on a regeneration interval. A few applications include random walks in random environment and additive functionals of recurrent Markov chains. The result is formulated in the p-variation settings, where a rough path version of Donsker’s Theorem is available under the second moment condition. The key renewal theorem is applied to obtain an optimal moment condition.
  • Thumbnail Image
    Item
    Limit theorems for Lévy flights on a 1D Lévy random medium
    ([Madralin] : EMIS ELibEMS, 2021) Stivanello, Samuele; Bet, Gianmarco; Bianchi, Alessandra; Lenci, Marco; Magnanini, Elena
    We study a random walk on a point process given by an ordered array of points (ωk,k∈Z) on the real line. The distances ωk+1−ωk are i.i.d. random variables in the domain of attraction of a β-stable law, with β∈(0,1)∪(1,2). The random walk has i.i.d. jumps such that the transition probabilities between ωk and ωℓ depend on ℓ−k and are given by the distribution of a Z-valued random variable in the domain of attraction of an α-stable law, with α∈(0,1)∪(1,2). Since the defining variables, for both the random walk and the point process, are heavy-tailed, we speak of a Lévy flight on a Lévy random medium. For all combinations of the parameters α and β, we prove the annealed functional limit theorem for the suitably rescaled process, relative to the optimal Skorokhod topology in each case. When the limit process is not càdlàg, we prove convergence of the finite-dimensional distributions. When the limit process is deterministic, we also prove a limit theorem for the fluctuations, again relative to the optimal Skorokhod topology.
  • Thumbnail Image
    Item
    Random walks in random hypergeometric environment
    ([Madralin] : EMIS ELibEMS, 2020) Orenshtein, Tal; Sabot, Christophe
    We consider one-dependent random walks on Zd in random hypergeometric environment for d≥3. These are memory-one walks in a large class of environments parameterized by positive weights on directed edges and on pairs of directed edges which includes the class of Dirichlet environments as a special case. We show that the walk is a.s. transient for any choice of the parameters, and moreover that the return time has some finite positive moment. We then give a characterization for the existence of an invariant measure for the process from the point of view of the walker which is absolutely continuous with respect to the initial distribution on the environment in terms of a function κ of the initial weights. These results generalize [Sab11] and [Sab13] on random walks in Dirichlet environment. It turns out that κ coincides with the corresponding parameter in the Dirichlet case, and so in particular the existence of such invariant measures is independent of the weights on pairs of directed edges, and determined solely by the weights on directed edges.
  • Thumbnail Image
    Item
    Lower large deviations for geometric functionals
    ([Madralin] : EMIS ELibEMS, 2020) Hirsch, Christian; Jahnel, Benedikt; Tóbiás, András
    This work develops a methodology for analyzing large-deviation lower tails associated with geometric functionals computed on a homogeneous Poisson point process. The technique applies to characteristics expressed in terms of stabilizing score functions exhibiting suitable monotonicity properties. We apply our results to clique counts in the random geometric graph, intrinsic volumes of Poisson–Voronoi cells, as well as power-weighted edge lengths in the random geometric, k-nearest neighbor and relative neighborhood graph.