Results 1 to 10 of about 3,299 (70)
Planar random-cluster model: scaling relations
Forum of Mathematics, Pi, 2022 This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in [1,4]$ using novel coupling techniques.
Hugo Duminil-Copin, Ioan Manolescu
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KP governs random growth off a 1-dimensional substrate
Forum of Mathematics, Pi, 2022 The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation. This is derived algebraically from a Fredholm determinant obtained
Jeremy Quastel, Daniel Remenik
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Asymptotics of pure dimer coverings on rail yard graphs
Forum of Mathematics, Sigma, 2023 We study the asymptotic limit of random pure dimer coverings on rail yard graphs when the mesh sizes of the graphs go to 0. Each pure dimer covering corresponds to a sequence of interlacing partitions starting with an empty partition and ending in an ...
Zhongyang Li, Mirjana Vuletić
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Fluctuations for Some Nonstationary Interacting Particle Systems via Boltzmann–Gibbs Principle
Forum of Mathematics, Sigma, 2023 Conjecture II.3.6 of Spohn in [47] and Lecture 7 of Jensen–Yau in [35] ask for a general derivation of universal fluctuations of hydrodynamic limits in large-scale stochastic interacting particle systems. However, the past few decades have witnessed only
Kevin Yang
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One-sided reflected Brownian motions and the KPZ fixed point
Forum of Mathematics, Sigma, 2020 We consider the system of one-sided reflected Brownian motions that is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of ...
Mihai Nica +2 more
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On the heapability of finite partial orders [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing such a ...
János Balogh +4 more
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Correlations in totally symmetric self‐complementary plane partitions
Transactions of the London Mathematical Society, 2021 Totally symmetric self‐complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well‐known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in 1/12 of a hexagon with free ...
Arvind Ayyer, Sunil Chhita
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Soliton Decomposition of the Box-Ball System
Forum of Mathematics, Sigma, 2021 The box-ball system (BBS) was introduced by Takahashi and Satsuma as a discrete counterpart of the Korteweg-de Vries equation. Both systems exhibit solitons whose shape and speed are conserved after collision with other solitons.
Pablo A. Ferrari +3 more
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Sampling From A Manifold [PDF]
, 2012 We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to Neyman's ...
Mehrdad Shahshahani +5 more
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COVER TIME FOR THE FROG MODEL ON TREES
Forum of Mathematics, Sigma, 2019 The frog model is a branching random walk on a graph in which particles branch only at unvisited sites. Consider an initial particle density of $\unicode[STIX]{x1D707}$ on the full $d$-ary tree of height $n$.
CHRISTOPHER HOFFMAN +2 more
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