# , Vertex Isoperimetry and Concentration

@article{Bobkov2000VI, title={, Vertex Isoperimetry and Concentration}, author={Sergey G. Bobkov and Christian Houdr{\'e} and Prasad Tetali}, journal={Combinatorica}, year={2000}, volume={20}, pages={153-172} }

. This approach refines results relating the spectral gap of a graph to the so-called magnification of a graph. A concentration result involving is also derived.

## 43 Citations

Expansion And Isoperimetric Constants For Product Graphs

- Mathematics, Computer ScienceComb.
- 2006

Vertex and edge isoperimetric constants of graphs are studied using a functional-analytic approach and the growth properties of these constants is analyzed.

Isoperimetric Invariants For Product Markov Chains and Graph Products

- Mathematics, Computer ScienceComb.
- 2004

Bounds on some isoperimetric constants of the Cartesian product of Markov chains are obtained in terms of related isoperimetric quantities of the individual chains.

Isoperimetric and related bounds on configuration spaces

- Mathematics
- 2008

Using finite difference operators, we define a notion of boundary and surface measure for configuration sets under Poisson measures. A Margulis-Russo type identity and a co-area formula are stated…

Surface measures and related functional inequalities on configuration spaces

- Mathematics
- 2019

Using finite difference operators, we define a notion of boundary and surface measure for configuration sets under Poisson measures. A Margulis-Russo type identity and a co-area formula are stated…

Concentration of Measure for Products of Markov Kernels and Graph Products via Functional Inequalities

- Computer Science, MathematicsCombinatorics, Probability and Computing
- 2001

We present versions of concentration inequalities for products of Markov kernels and graph products. We also present discussions of a variety of consequences such as sharp upper bounds, in terms of…

Surveys in Differential Geometry

- Mathematics
- 1999

The purpose of this article is to survey the recent progress made on estimating positive eigenvalues of Laplacian on hyperbolic Riemann surfaces in the case of congruence subgroups in connection with…

Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels

- Mathematics
- 2006

We show how the evolving set methodology of Morris and Peres can be used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel. This leads to sharp versions of several…

On the isoperimetric spectrum of graphs and its approximations

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. B
- 2010

This paper focuses on the nth mean isoperimetric constant of a directed graph as the minimum of the mean outgoing normalized flows from a given set of n disjoint subsets of the vertex set of the graph, and defines and presents examples for the concept of a supergeometric graph as a graph whose mean isoperative constants are attained on partitions at all levels.

Faster Mixing by Isoperimetric Inequalities

- Mathematics
- 2003

Faster Mixing by Isoperimetric Inequalities

Multi-Way Expanders and Imprimitive Group Actions on Graphs

- Mathematics
- 2016

For n at least 2, the concept of n-way expanders was defined by various researchers. Bigger n gives a weaker notion in general, and 2-way expanders coincide with expanders in usual sense. Koji…

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