%0 Generic %1 kondratiev2017selfregulation %A Kondratiev, Yuri %A Kozitsky, Yuri %D 2017 %K Bolker-Pacala spatial_demography spatial_models %T Self-regulation in continuum population models %U http://arxiv.org/abs/1702.02920 %X We study the Markov dynamics of an infinite birth-and-death system of point entities placed in $R^d$, in which the constituents disperse and die, also due to competition. Assuming that the dispersal and competition kernels are just continuous and integrable we prove that the evolution of states of this model preserves their sub-Poissonicity, and hence the local self-regulation (suppression of clustering) takes place. Upper bounds for the correlation functions of all orders are also obtained for both long and short dispersals, and for all values of the intrinsic mortality rate $m0$.

@misc{kondratiev2017selfregulation, abstract = {We study the Markov dynamics of an infinite birth-and-death system of point entities placed in $\mathbb{R}^d$, in which the constituents disperse and die, also due to competition. Assuming that the dispersal and competition kernels are just continuous and integrable we prove that the evolution of states of this model preserves their sub-Poissonicity, and hence the local self-regulation (suppression of clustering) takes place. Upper bounds for the correlation functions of all orders are also obtained for both long and short dispersals, and for all values of the intrinsic mortality rate $m\geq 0$.}, added-at = {2020-07-22T20:49:30.000+0200}, author = {Kondratiev, Yuri and Kozitsky, Yuri}, biburl = {https://www.bibsonomy.org/bibtex/266610c5888d1f84da5fcb6ad07d1a3a3/peter.ralph}, interhash = {80f1cd0410a79475172a0eb86764ac1d}, intrahash = {66610c5888d1f84da5fcb6ad07d1a3a3}, keywords = {Bolker-Pacala spatial_demography spatial_models}, note = {Comment: arXiv admin note: substantial text overlap with arXiv:1607.05871}, timestamp = {2020-07-22T20:49:30.000+0200}, title = {Self-regulation in continuum population models}, url = {http://arxiv.org/abs/1702.02920}, year = 2017 }