Fetching the paper…
Reading the bibliography…
We prove the following estimate for the spectrum of the normalized Laplace operator $\Delta$ on a finite graph $G$, \begin{equation*}1- (1- k[t])^{\frac{1}{t}}\leq \lambda_1 \leq \cdots \leq \lambda_{N-1}\leq 1+ (1- k[t])^{\frac{1}{t}}, \,\forall \,\,\text{integers}\,\, t\geq 1.
A. Lichnerowicz,
1958
Earlier work this paper cites.
J. M. Hammersley,
1962
Earlier work this paper cites.
P. Li and S. T. Yau,
1980
Earlier work this paper cites.
I. Chavel,
1984
Earlier work this paper cites.
M. Chen and F. Wang,
1994
Earlier work this paper cites.
R. Bubley and M. E. Dyer,
1997
Earlier work this paper cites.
M. Chen,
1997
Earlier work this paper cites.
F. R. K. Chung,
1997
Earlier work this paper cites.
M. Chen,
1998
Earlier work this paper cites.
D. J. Watts and S. H. Strogatz,
1998
Cited alongside, same era.
L. C. Evans,
1999
Cited alongside, same era.
P. Auscher and T. Coulhon and A. Grigor’yan,
2003
Cited alongside, same era.
C. Villani,
2003
Cited alongside, same era.
Y. Peres,
2005
Cited alongside, same era.
K.-T. Sturm,
2006
Cited alongside, same era.
S.-I. Ohta,
2007
Cited alongside, same era.
A. Grigor’yan,
2009
Later among the works it cites.
D. A. Levin, Y. Peres and E. L. Wilmer,
2009
Later among the works it cites.
J. Lott and C. Villani,
2009
Later among the works it cites.
Y. Ollivier,
2009
Later among the works it cites.
C. Villani,
2009
Later among the works it cites.
A. Joulin and Y. Ollivier,
2010
Later among the works it cites.
Y. Lin and S. T. Yau,
2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2009
Cited alongside, same era.
Cited in the paper.
Cited in the paper.
Y. Ollivier, A survey of Ricci curvature for metric spaces and Markov chains, in: M. Kotani, M. Hino and T. Kumagai (Eds.), Probabilistic approach to geometry, Adv. Stud. Pure Math. 57, Math. Soc. Japan, Tokyo, 2010, pp. 343-381
2010
Later among the works it cites.