Results 21 to 30 of about 4,858 (93)

Harry Kesten’s work in probability theory [PDF]

Probability theory and related fields, 2020
We survey the published work of Harry Kesten in probability theory, with emphasis on his contributions to random walks, branching processes, percolation, and related topics.
G. Grimmett
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Local Kesten–McKay Law for Random Regular Graphs [PDF]

Communications in Mathematical Physics, 2016
We study the adjacency matrices of random d-regular graphs with large but fixed degree d. In the bulk of the spectrum $${[-2\sqrt{d-1}+\varepsilon, 2\sqrt{d-1}-\varepsilon]}$$[-2d-1+ε,2d-1-ε] down to the optimal spectral scale, we prove that the Green’s ...
R. Bauerschmidt, Jiaoyang Huang, H. Yau
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Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues [PDF]

Advances in Applied Probability, 2017
We study the tail asymptotic of subexponential probability densities on the real line. Namely, we show that the n-fold convolution of a subexponential probability density on the real line is asymptotically equivalent to this density multiplied by n.
D. Finkelshtein, Pasha Tkachov
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Kesten–McKay law for the Markoff surface mod p [PDF]

Annales Henri Lebesgue, 2018
For each prime $p$, we study the eigenvalues of a 3-regular graph on roughly $p^2$ vertices constructed from the Markoff surface. We show they asymptotically follow the Kesten-McKay law, which also describes the eigenvalues of a random regular graph. The
M. D. Courcy-Ireland, Michael Magee
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Kesten–McKay Law for Random Subensembles of Paley Equiangular Tight Frames [PDF]

Constructive approximation, 2019
We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish concerning the distribution of the singular values of random subensembles of Paley equiangular tight frames.
Mark Magsino, D. Mixon, Hans Parshall
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Kesten’s theorem for uniformly recurrent subgroups [PDF]

Ergodic Theory and Dynamical Systems, 2018
We prove a lower bound on the difference between the spectral radius of the Cayley graph of a group $G$ and the spectral radius of the Schreier graph $H\backslash G$ for any subgroup $H$ .
Mikołaj Frączyk
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The Tightness of the Kesten–Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations [PDF]

, 2017
It is well known that reconstruction problems, as the interdisciplinary subject, have been studied in numerous contexts including statistical physics, information theory and computational biology, to name a few.
Wenjian Liu, S. Jammalamadaka, Ning Ning
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Kesten's incipient infinite cluster and quasi-multiplicativity of crossing probabilities [PDF]

, 2016
In this paper we consider Bernoulli percolation on an infinite connected bounded degrees graph $G$. Assuming the uniqueness of the infinite open cluster and a quasi-multiplicativity of crossing probabilities, we prove the existence of Kesten's incipient ...
D. Basu, A. Sapozhnikov
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A note on the Kesten--Grincevi\v{c}ius--Goldie theorem [PDF]

, 2015
Consider the perpetuity equation $X \stackrel{\mathcal{D}}{=} A X + B$, where $(A,B)$ and $X$ on the right-hand side are independent. The Kesten--Grincevi\v{c}ius--Goldie theorem states that $P \{ X > x \} \sim c x^{-\kappa}$ if $E A^\kappa = 1$, $E A ...
P. Kevei
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Community detection and stochastic block models: recent developments [PDF]

Foundations and Trends in Communications and Information Theory, 2017
The stochastic block model (SBM) is a random graph model with planted clusters. It is widely employed as a canonical model to study clustering and community detection, and provides generally a fertile ground to study the statistical and computational ...
E. Abbe
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