##### Department of Mathematics,

University of California San Diego

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### Math 288: Probability & Statistics

## Nikita Gladkov

#### UCLA (gladkovna@gmail.com)

## Inequalities for connectivity events in Bernoulli percolation

##### Abstract:

In Bernoulli percolation, events such as "two vertices are connected by an open path" naturally emerge. In this talk, I will explore the dependencies between these events for various vertex pairs and derive key FKG-type inequalities governing their probabilities and explain the relevance of these inequalities to the recent disproof of the Bunkbed Conjecture.

Morris Ang

### November 7, 2024

### 11:00 AM

APM 6402

Research Areas

Probability Theory****************************