Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping

2021 ◽  
Vol 31 (4) ◽  
pp. 259-269
Author(s):  
Vladimir O. Mironkin
Keyword(s):  
Connected Component ◽  
Arbitrary Vertex ◽  
Random Mapping

Abstract The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.

The largest connected component in a random mapping

1994 ◽  
Vol 5 (1) ◽  
pp. 73-94 ◽  
Author(s):  
Jerzy Jaworski ◽  
Ljuben Mutafchiev
Keyword(s):  
Connected Component ◽  
Random Mapping

scholarly journals Non Kählerian surfaces with a cycle of rational curves

2021 ◽  
Vol 8 (1) ◽  
pp. 208-222
Author(s):  
Georges Dloussky
Keyword(s):  
Deformation Theory ◽  
Complex Surface ◽  
Rational Curves ◽  
Intersection Form ◽  
Connected Component ◽  
Hirzebruch Surface ◽  
Compact Complex Surface ◽  
A Chain

Abstract Let S be a compact complex surface in class VII0 + containing a cycle of rational curves C = ∑Dj . Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C ′ then C ′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj . In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.

scholarly journals On orbits of the automorphism group on an affine toric variety

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Ivan Arzhantsev ◽  
Ivan Bazhov
Keyword(s):  
Automorphism Group ◽  
Vector Space ◽  
Toric Variety ◽  
Connected Component ◽  
Linear Action

AbstractLet X be an affine toric variety. The total coordinates on X provide a canonical presentation $$\bar X \to X$$ of X as a quotient of a vector space $$\bar X$$ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

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