- Tytuł:
- Free probability induced by electric resistance networks on energy Hilbert spaces
- Autorzy:
-
Cho, I.
Jorgensen, P. E. T. - Powiązania:
- https://bibliotekanauki.pl/articles/254830.pdf
- Data publikacji:
- 2011
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
directed graphs
graph groupoids
electric resistance networks
ERN-groupoids
energy Hilbert spaces
ERN-algebras
free moments
free cumulants - Opis:
- We show that a class of countable weighted graphs arising in the study of electric resistance networks (ERNs) are naturally associated with groupoids. Starting with a fixed ERN, it is known that there is a canonical energy form and a derived energy Hilbert space Hε. From Hε, one then studies resistance metrics and boundaries of the ERNs. But in earlier research, there does not appear to be a natural algebra of bounded operators acting on Hε. With the use of our ERN-groupoid, we show that Hε may be derived as a representation Hilbert space of a universal representation of a groupoid algebra [formula], and we display other representations. Among our applications, we identify a free structure of [formula] in terms of the energy form.
- Źródło:
-
Opuscula Mathematica; 2011, 31, 4; 549-598
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł