Properties of an asymmetric annihilation process (Prof. Volker Strehl)
Sprache des Titels:
In recent work the physicists A. Ayyer and K. Mallik (C.E.A. Saclay) introduced
a model for an asymmetric exclusion process (like the famous TASEP model)
which in addition to previous studies includes the possibility for pairwise
annihilation of particles. They investigated combinatorial and stochastic
of this model in detail, but a major problem remained unresolved: computing
the eigenvalues of this process -- but they came up with an intriguing
A proof of this conjecture (and a far more general statement) will be outlined
in this talk. In addition, a generalized version of the partition function and
transfer matrices for this process will be presented, as well as a conjecture
about rational functions related to shifted Young tableaux.
It should be mentioned that although the proof of the eigenvalue conjecture
is now completely ``classical'', its discovery was guided by heavy
assistance of computer algebra.
Part of this work was done in collaboration with A. Ayyer.