Former Research Group
Random Spatial Processes
Our research was in probability theory with special emphasis on geometric aspects of random processes on graphs. Particular interests were in phase transitions, critical phenomena, asymptotic laws, self-organization.
Research Group Leader
01.10.12
31.12.17
Artem Sapozhnikov
Universität Leipzig
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Publications
inJournal
2018On Brownian motion, simple paths, and loops
In: Probability theory and related fieldsinBook
2018Convergence time of probabilistic cellular automata on the torus
In: Probabilistic cellular automata : theory, applications and future perspectives. Papers based on the workshop held at EURANDOM, TU Eindhoven, June 2013inJournal
2017Crossing probabilities for critical Bernoulli percolation on slabs
In: Annales de l'Institut Henri Poincaré / BAcademic
2017Generalizations and interpretations of incipient infinite cluster measure on planar lattices and slabs
Dissertation, Universität LeipziginJournal
2017Kesten's incipient infinite cluster and quasi-multiplicativity of crossing probabilities
In: Electronic communications in probabilityinJournal
2017Two observations on the capacity of the range of simple random walks on \(\mathbb{Z}^3\) and \(\mathbb{Z}^4\)
In: Electronic communications in probabilityinJournal
2017Random walks on infinite percolation clusters in models with long-range correlations
In: The annals of probabilityinJournal
2016Almost empty monochromatic triangles in planar point sets
In: Discrete applied mathematicsinBook
2016Markov loops in discrete spaces
In: Probability and statistical physics in St. PetersburginJournal
2016Phase transition in loop percolation
In: Probability theory and related fieldsinJournal
2016Supercritical loop percolation on \(\mathbb{Z}^d\) for \(d\geq 3\)
In: Stochastic processes and their applicationsinJournal
2016Quenched invariance principle for simple random walk on clusters in correlated percolation models
In: Probability theory and related fieldsinJournal
2016Mixing time for the random walk on the range of the random walk on tori
In: Electronic journal of probabilityinJournal
2016Absorbing-state phase transition in biased activated random walk
In: Electronic journal of probabilityinJournal
2015A convergence result on the lengths of Markovian loops
In: Electronic communications in probabilityinJournal
2015Loop cluster on discrete circles
In: Electronic journal of probabilityAcademic
2015Absorbing-state phase transition in activated random walk and probabilistic cellular automata
Dissertation, Universität LeipziginJournal
2015Critical probabilities and convergence time of percolation probabilistic cellular automata
In: Journal of statistical physicsinBook
2014Multi-occupation field generates the Borel-sigma-field of loops
In: Seminaire de probabilites XLVIBook
2014