# On the randomised stability constant for inverse problems

## TL;DR

This paper introduces the randomised stability constant for inverse problems, extending the concept of the randomised observability constant, and explores its properties and implications for practical inversion methods.

## Contribution

It generalizes the randomised observability constant to a broader class of inverse problems and analyzes its properties and practical significance.

## Key findings

- Defines the randomised stability constant for inverse problems.
- Analyzes properties of the new stability constant.
- Discusses implications for practical inversion techniques.

## Abstract

In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave equation. We study the main properties of the randomised stability constant and discuss the implications for the practical inversion, which are not straightforward.