## Talagrand’s Concentration Inequality

We prove a powerful inequality which provides very tight gaussian tail bounds “$e^{-ct^2}$” for probabilities on product state spaces $\Omega^n$. Talagrand’s Inequality has found lots of applications in probability and combinatorial optimization and, if one can apply it, it generally outperforms inequalities like Azzuma-Hoeffding.

## Lecture 0. Some Basic Maths for Actuarial Students

We will regularly need to employ certain calculations. In MATH10951 the context might vary but the maths varies much less. These notes are more of a background check on prequisties. We cover

• Power, the exponential, logarithms, the (natural) logarithm.
• Arithmetic and Geometric progressions.