@article{64213,
  abstract     = {{A layered graph G^× is the Cartesian product of a graph G = (V, E) with the linear graph Z, e.g. Z^× is the 2D square lattice Z^2. For Bernoulli percolation with parameter p ∈ [0, 1] on G^× one intuitively would expect that P_p((o, 0) ↔ (v, n)) ≥ P_p((o, 0) ↔ (v, n + 1)) for all o, v ∈ V and n ≥ 0. This is reminiscent of the better known bunkbed conjecture. Here
we introduce an approach to the above monotonicity conjecture that makes use of a Markov chain building the percolation pattern layer by layer. In case of finite G we thus can show that for some N ≥ 0 the above holds
for all n ≥ N o, v ∈ V and p ∈ [0, 1]. One might hope that this Markov chain approach could be useful for other problems concerning Bernoulli percolation on layered graphs}},
  author       = {{König, Philipp and Richthammer, Thomas}},
  issn         = {{0304-4149}},
  journal      = {{Stochastic Processes and their Applications}},
  publisher    = {{Elsevier BV}},
  title        = {{{Monotonicity properties for Bernoulli percolation on layered graphs— A Markov chain approach}}},
  doi          = {{10.1016/j.spa.2024.104549}},
  volume       = {{181}},
  year         = {{2024}},
}

@article{43493,
  abstract     = {{We consider a measure given as the continuum limit of a one-dimensional Ising model with long-range translationally invariant interactions. Mathematically, the measure can be described by a self-interacting Poisson driven jump process. We prove a correlation inequality, estimating the magnetic susceptibility of this model, which holds for small norm of the interaction function. The bound on the magnetic susceptibility has applications in quantum field theory and can be used to prove existence of ground states for the spin boson model.}},
  author       = {{Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}},
  issn         = {{0304-4149}},
  journal      = {{Stochastic Processes and their Applications}},
  pages        = {{60--79}},
  publisher    = {{Elsevier BV}},
  title        = {{{Correlation bound for a one-dimensional continuous long-range Ising model}}},
  doi          = {{10.1016/j.spa.2021.12.010}},
  volume       = {{146}},
  year         = {{2021}},
}

@article{40218,
  author       = {{Lasser, R. and Rösler, Margit}},
  issn         = {{0304-4149}},
  journal      = {{Stochastic Processes and their Applications}},
  keywords     = {{Applied Mathematics, Modeling and Simulation, Statistics and Probability}},
  number       = {{2}},
  pages        = {{279--293}},
  publisher    = {{Elsevier BV}},
  title        = {{{Linear mean estimation of weakly stationary stochastic processes under the aspects of optimality and asymptotic optimality}}},
  doi          = {{10.1016/0304-4149(91)90095-t}},
  volume       = {{38}},
  year         = {{1991}},
}