@article{CaselFischbeckFriedrichetal.2022,
  author    = {Casel, Katrin and Fischbeck, Philipp and Friedrich, Tobias and G{\"o}bel, Andreas and Lagodzinski, J. A. Gregor},
  title     = {Zeros and approximations of Holant polynomials on the complex plane},
  series = {Computational complexity : CC},
  volume    = {31},
  journal   = {Computational complexity : CC},
  number    = {2},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1016-3328},
  doi       = {10.1007/s00037-022-00226-5},
  pages     = {52},
  year      = {2022},
  abstract  = {We present fully polynomial time approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures known as polymers in statistical physics. Our method involves establishing zero-free regions for the partition functions of polymer models and using the most significant terms of the cluster expansion to approximate them. Results of our technique include new approximation and sampling algorithms for a diverse class of Holant polynomials in the low-temperature regime (i.e. small external field) and approximation algorithms for general Holant problems with small signature weights. Additionally, we give randomised approximation and sampling algorithms with faster running times for more restrictive classes. Finally, we improve the known zero-free regions for a perfect matching polynomial.},
  language  = {en}
}
@article{FischerKeller2021,
  author    = {Fischer, Florian and Keller, Matthias},
  title     = {Riesz decompositions for Schr{\"o}dinger operators on graphs},
  series = {Journal of mathematical analysis and applications},
  volume    = {495},
  journal   = {Journal of mathematical analysis and applications},
  number    = {1},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0022-247X},
  doi       = {10.1016/j.jmaa.2020.124674},
  pages     = {22},
  year      = {2021},
  abstract  = {We study superharmonic functions for Schrodinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into a harmonic and a potential part. The second one decomposes a superharmonic function into a sum of superharmonic functions with certain upper bounds given by prescribed superharmonic functions. As application we show a Brelot type theorem.},
  language  = {en}
}