# Exact renormalization groups and transportation of measures

@inproceedings{Shenfeld2022ExactRG, title={Exact renormalization groups and transportation of measures}, author={Yair Shenfeld}, year={2022} }

. This note provides a new perspective on Polchinski’s equation for the exact renormalization group by explaining how it gives rise, via the multiscale Bakry-´Emery criterion, to Lipschitz transport maps between Gaussian free ﬁelds and Euclidean quantum ﬁeld theories. Consequently, many functional inequalities can be veriﬁed for the latter ﬁeld theories, going beyond the current known results.

## One Citation

### Behavior of the Poincar{\'e} constant along the Polchinski renormalization flow

- Mathematics
- 2022

We control the behavior of the Poincar´e constant along the Polchinski renormalization ﬂow using a dynamic version of Γ-calculus. We also treat the case of higher order eigenvalues. Our method…

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