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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Space-time localisation for the dynamic $\Phi^4_3$ model

## Space-time localisation for the dynamic $\Phi^4_3$ modelAdd to your list(s) Download to your calendar using vCal - Hendrik Weber (University of Bath)
- Thursday 13 December 2018, 09:00-10:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. SRQW03 - Scaling limits & SPDEs: recent developments and future directions We prove an a priori bound for solutions of the dynamic $\Phi^4_3$ equation. This bound provides a control on solutions on a compact space-time set only in terms of the realisation of the noise on an enlargement of this set, and it does not depend on any choice of space-time boundary conditions. <span><br>We treat the large and small scale behaviour of solutions with completely different arguments. </span> For small scales we use bounds akin to those presented in Hairer's theory of regularity structures. For large scales we use a PDE argument based on the maximum principle. Both regimes are connected by a solution-dependent regularisation procedure. <br>The fact that our bounds do not depend on space-time boundary conditions makes them useful for the analysis of large scale properties of solutions. They can for example be used in a compactness argument to construct solutions on the full space and their invariant measures. <br><span><br>Joint work with A. Moinat.</span> This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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