Robust constraints on Lorentz Invariance Violation from H.E.S.S., MAGIC and VERITAS data combination

Gamma-Ray bursts, flaring active galactic nuclei and pulsars are distant and energetic astrophysical sources, detected up to tens of TeV with Imaging Atmospheric Cherenkov Telescopes (IACTs). Due to their high variability, they are the most suitable sources for energy-dependent time-delay searches related to Lorentz Invariance Violation (LIV) predicted by some Quantum Gravity (QG) models. However, these studies require large datasets. A working group between the three major IACTs ground experiments - H.E.S.S., MAGIC and VERITAS - has been formed to address this issue and combine for the first time all the relevant data collected by the three experiments in a joint analysis. This proceeding will review the new standard combination method. The likelihood technique used to deal with data from different source types and instruments will be presented, as well as the way systematic uncertainties are taken into account. The method has been developed and tested using simulations based on published source observations from the three experiments. From these simulations, the performance of the method will be assessed and new light will be shed on time delays dependencies with redshift.