4 citations · 10 across the 19 of their papers we have counts for
20 papers
From Kreweras walks to branching perimeter processes of percolated triangulations
Renan Gross, Emmanuel Kammerer, Frederik Ravn Klausen
In this note, using a result of Bernardi, Holden and Sun, we give an explicit geometric relation between the perimeter of the peeling process along the percolation interface of a t…
The End of the Double Random Current
Ulrik Thinggaard Hansen, Frederik Ravn Klausen
The Ising correlation function can be expressed in terms of connectivity probabilities of a random graph known as the double random current. In 2016, Duminil-Copin asked whether th…
The Supercritical Loop O(1) and Random Current models: Uniqueness and Mixing
Ulrik Thinggaard Hansen, Frederik Ravn Klausen
Much recent rigorous study of the classical ferromagnetic Ising model has been powered by its graphical representations, such as the random current and loop O(1) model (high temper…
Half-plane non-coexistence without FKG
Frederik Ravn Klausen, Noah Kravitz
For an edge percolation measure on the infinite square lattice, let (respectively, ) denote its marginal (respectively, the marginal of its planar d…
Powers in prime bases and a problem on central binomial coefficients
Sebastian Tim Holdum, Frederik Ravn Klausen, Peter Michael Reichstein Rasmussen
It is an open problem whether is divisible by 4 or 9 for all . In connection with this, we prove that for a fixed uneven the asymptotic density of '…
A simple proof of exponential decay for the near-critical planar Ising model
Jianping Jiang, Frederik Ravn Klausen
For the Ising model defined on at critical temperature with external field , we give a simple and elementary proof that its truncated two-point function…
A General Coupling for Ising Models and Beyond
Ulrik Thinggaard Hansen, Jianping Jiang, Frederik Ravn Klausen
The couplings between the Ising model and its graphical representations, the random-cluster, random current and loop models, are put on common footing through a gen…
Fault-tolerant quantum simulation of generalized Hubbard models
Andreas Juul Bay-Smidt, Frederik Ravn Klausen, Christoph Sünderhauf +3
Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum comput…
Non-uniqueness of phase transitions for graphical representations of the Ising model on tree-like graphs
Ulrik Thinggaard Hansen, Frederik Ravn Klausen, Peter Wildemann
We consider the graphical representations of the Ising model on tree-like graphs. We construct a class of graphs on which the loop model and the single random curre…
Random Problems in Mathematical Physics
Frederik Ravn Klausen
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematic…
Decoherence is an echo of Anderson localization in open quantum systems
Frederik Ravn Klausen, Simone Warzel
We study the time evolution of single-particle quantum states described by a Lindblad master equation with local terms. By means of a geometric resolvent equation derived for Lindb…
Going Beyond Gadgets: The Importance of Scalability for Analogue Quantum Simulators
Dylan Harley, Ishaun Datta, Frederik Ravn Klausen +4
Quantum hardware has the potential to efficiently solve computationally difficult problems in physics and chemistry to reap enormous practical rewards. Analogue quantum simulation…
The Uniform Even Subgraph and Its Connection to Phase Transitions of Graphical Representations of the Ising Model
Ulrik Thinggaard Hansen, Boris Kjær, Frederik Ravn Klausen
The uniform even subgraph is intimately related to the Ising model, the random-cluster model, the random current model, and the loop (1) model. In this paper, we first…
Stochastic cellular automaton model of culture formation
Frederik Ravn Klausen, Asbjørn Bækgaard Lauritsen
We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantifi…
Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices
Frederik Ravn Klausen
It is shown that generators of single-particle, translation-invariant Lindblad operators on the infinite line are unitarily equivalent to direct integrals of finite-range bi-infini…
Strict monotonicity, continuity and bounds on the Kertész line for the random-cluster model on
Ulrik Thinggaard Hansen, Frederik Ravn Klausen
Ising and Potts models can be studied using the Fortuin-Kasteleyn representation through the Edwards-Sokal coupling. This adapts to the setting where the models are exposed to an e…
Mass scaling of the near-critical 2D Ising model using random currents
Frederik Ravn Klausen, Aran Raoufi
We examine the Ising model at its critical temperature with an external magnetic field on for . A new proof of exponential decay of the…
On monotonicity and couplings of random currents and the loop--model
Frederik Ravn Klausen
Using recent couplings we provide counterexamples to monotonicity properties of percolation models related to graphical representations of the Ising model. We further prove a new c…
Combinatorial classification of quantum lens spaces
Peter Lunding Jensen, Frederik Ravn Klausen, Peter M. R. Rasmussen
We answer the question of how large the dimension of a quantum lens space must be, compared to the primary parameter , for the isomorphism class to depend on the secondary param…
On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence
Sebastian Tim Holdum, Frederik Ravn Klausen, Peter Michael Reichstein Rasmussen
We prove some cases of a conjecture by Farhi on the representation of every positive integer as the sum of three terms of the sequence . Th…