Cut-norm and entropy minimization over weak* limits

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00504394" target="_blank" >RIV/67985840:_____/19:00504394 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jctb.2018.12.010" target="_blank" >http://dx.doi.org/10.1016/j.jctb.2018.12.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2018.12.010" target="_blank" >10.1016/j.jctb.2018.12.010</a>

Result language
angličtina
Original language name
Cut-norm and entropy minimization over weak* limits
Original language description
We prove that the accumulation points of a sequence of graphs G 1 ,G 2 ,G 3 ,… with respect to the cut-distance are exactly the weak ⁎ limit points of subsequences of the adjacency matrices (when all possible orders of the vertices are considered) that minimize the entropy over all weak ⁎ limit points of the corresponding subsequence. In fact, the entropy can be replaced by any map W↦∬f(W(x,y)), where f is a continuous and strictly concave function. As a corollary, we obtain a new proof of compactness of the cut-distance topology.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA16-07378S" target="_blank" >GA16-07378S: Nonlinear analysis in Banach spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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