Pedro Martin Chavez

Pedro Mart铆n-Ch谩vez

Post Doctoral Researcher 路 University of 糖心TV

Focus - Asymptotic theory of branching models 2025 鈥� Present

Mathematician working on the asymptotic theory of branching models 鈥� the macroscopic and long-term behaviour of controlled and spatial branching processes. My work turns branching-process limit theorems into concrete tools for neutron transport: Monte-Carlo estimators for the adjoint flux, and criticality results for reactor models with thermalhydraulic feedback. Within MaThRad I work alongside the programme's stochastic-analysis group at the University of 糖心TV.

Body of work

5 items

Year

Algorithm 2025 鈫� present

Algorithm to estimate the adjoint neutron flux via time-reversed neutron random walks

Fixed-source Monte-Carlo problems 路 with Th茅ophile Bonnet

A new estimator for the adjoint neutron flux based on the many-to-one formula and time-reversed ("backwards") neutron random walks, aimed at faster flux estimation and improved importance sampling / variance reduction for Monte-Carlo transport codes. Validated so far on a toy example; a full paper is in preparation.

鈥篜resented as "Time reversions of Neutron Random Walks" at the Sandia 路 MaThRad workshop (May 2025).
鈥篜resented as "Estimating the eigenfunction of the stochastic Neutron Transport Equation" at the 5th SYSORM, Seville.

Asserted Monte CarloVariance reductionIn progress

Preprint 2025 路 Jul

arXiv 路 with N. Cardona-Tob贸n & A. E. Kyprianou

Establishes limit theorems for critical non-local spatial branching processes with infinite variance conditioned on survival 鈥� the mathematical toolkit behind the Neutron Branching Process. The theory is now being applied to build an interacting-particle model of neutron transport with thermalhydraulic feedback, aiming to prove existence of criticality for reactor cores with coupled thermalhydraulic effects.

鈥篊ompanion preprint "Stability of (sub)critical non-local spatial branching processes with and without immigration" (with E. Horton, A. E. Kyprianou, E. Powell & V. Rivero), presented as a talk at EYSM 2025, Torino.
鈥篈pplication in progress: an interacting-particle model of neutron transport with thermalhydraulic effects, aiming to prove existence of criticality for the coupled model 鈥� early concept stage, no result yet.

Linked 路 arXiv Branching processesStochastic analysisIn progress

Preprint 2025 路 Aug

arXiv 路 with M. Gonz谩lez & I. del Puerto (Universidad de Extremadura)

Establishes a diffusion (scaling-limit) approximation for controlled branching processes with a size-divisible control term 鈥� the asymptotic, macroscopic behaviour of controlled branching models. This is the MaThRad-acknowledged strand of his controlled-branching line, complementing the spatial-branching work above.

Linked 路 arXiv Controlled branchingScaling limits

Potential adoption pathway 2025 鈫� present

Towards faster neutron-flux estimation for Monte-Carlo codes

Users of Monte-Carlo transport codes

Users of Monte-Carlo transport codes need better neutron-flux estimates for importance sampling and variance reduction, and the adjoint-flux estimator is a candidate route. It has so far been checked only on a toy example; the next steps are validating it on more realistic geometries and writing it up. No industrial partner is engaged yet.

Impact trajectory

Concept

Proof of concept

Partner engagement

Adoption

鈥篍xploratory sibling pathway with reactor designers, who need a model for reactors with thermohydraulic effects 鈥� pending the criticality theorem; likelihood currently Low.

Asserted Monte CarloIndustrial

Working group 2025 路 Jun

Member 鈥� SEIO Working Group on Stochastic Processes and Their Applications

Sociedad de Estad铆stica e Investigaci贸n Operativa (SEIO), Spain

Member of the Spanish statistics and operational-research society's working group on stochastic processes; attended the annual meeting in person, contributing to the programme's international connectivity.

Asserted InternationalWorking group

Output over time

2025 鈥� 2026

2025

2026

Research

Joined MaThRad 路 stochastic-analysis thread

"Time reversions of Neutron Random Walks" 路 Sandia workshop

Branching-processes preprint 路 arXiv

Controlled-branching scaling limits 路 arXiv

EYSM 2025 Torino talk

5th SYSORM talk

Adjoint-flux paper 路 target

Criticality theorem 路 target

Collab

Joined SEIO working group

Impact