# Approximation for extinction probability of the contact process based on the Gr\"obner basis

## TL;DR

This paper introduces a novel method utilizing Gr"obner basis techniques to approximate the extinction probability of the one-dimensional contact process.

## Contribution

The paper presents a new approach for approximating extinction probabilities using algebraic methods, specifically Gr"obner bases, in the context of the contact process.

## Key findings

- Provides a series of approximations for extinction probability.
- Demonstrates effectiveness of algebraic methods in stochastic process analysis.
- Offers a potentially more accurate or efficient computational technique.

## Abstract

In this note we give a new method for getting a series of approximations for the extinction probability of the one-dimensional contact process by using the Gr\"obner basis.