## Electronic Communications in Probability

- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 68, 9 pp.

### The incipient giant component in bond percolation on general finite weighted graphs

#### Abstract

On a large finite connected graph let edges $e$ become “open” at independent random Exponential times of arbitrary rates $w_e$. Under minimal assumptions, the time at which a giant component starts to emerge is weakly concentrated around its mean.

#### Article information

**Source**

Electron. Commun. Probab., Volume 21 (2016), paper no. 68, 9 pp.

**Dates**

Received: 26 April 2016

Accepted: 7 September 2016

First available in Project Euclid: 21 September 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ecp/1474462208

**Digital Object Identifier**

doi:10.1214/16-ECP21

**Mathematical Reviews number (MathSciNet)**

MR3564215

**Zentralblatt MATH identifier**

1348.60136

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 05C80: Random graphs [See also 60B20]

**Keywords**

bond percolation incipient giant component concentration inequalities

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Aldous, David. The incipient giant component in bond percolation on general finite weighted graphs. Electron. Commun. Probab. 21 (2016), paper no. 68, 9 pp. doi:10.1214/16-ECP21. https://projecteuclid.org/euclid.ecp/1474462208