# Random Graphs from the Oriented Swap Process

## Presentation Type

Poster

## Faculty Advisor

Deepak Bal

## Access Type

Event

## Start Date

26-4-2024 11:15 AM

## End Date

26-4-2024 12:15 PM

## Description

The Oriented Swap Process (OSP) is a random process by which the sequence (1,2,...,n) is rearranged into (n,...,2,1) via a sequence of n(n-1)/2 randomly chosen adjacent position swaps. This process is akin to a randomized bubble sort. Angel, Holroyd and Romik discovered and proved many interesting phenomena related to the OSP. Every permutation of 1,2,...,n corresponds to a graph on n vertices whose edges represent the inversions in the permutation. The permutation (1,2,...,n) corresponds to the graph with no edges and (n,...,2,1) corresponds to the complete graph. Each intermediate step of the OSP corresponds to a different graph. In this project, we explore the sequence of graphs associated to the OSP.

Random Graphs from the Oriented Swap Process

The Oriented Swap Process (OSP) is a random process by which the sequence (1,2,...,n) is rearranged into (n,...,2,1) via a sequence of n(n-1)/2 randomly chosen adjacent position swaps. This process is akin to a randomized bubble sort. Angel, Holroyd and Romik discovered and proved many interesting phenomena related to the OSP. Every permutation of 1,2,...,n corresponds to a graph on n vertices whose edges represent the inversions in the permutation. The permutation (1,2,...,n) corresponds to the graph with no edges and (n,...,2,1) corresponds to the complete graph. Each intermediate step of the OSP corresponds to a different graph. In this project, we explore the sequence of graphs associated to the OSP.