Results 11 to 20 of about 67 (63)
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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Demonstratio Mathematica, 2021 Keller-Segel chemotaxis model is described by a system of nonlinear partial differential equations: a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration.
Slimani Ali +2 more
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A rigorous derivation of the Hamiltonian structure for the Vlasov equation
Forum of Mathematics, Sigma, 2023 We consider the Vlasov equation in any spatial dimension, which has long been known [ZI76, Mor80, Gib81, MW82] to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie–Poisson type.
Joseph K. Miller +4 more
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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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Forum of Mathematics, Pi, 2019 In last passage percolation models lying in the Kardar–Parisi–Zhang (KPZ) universality class, the energy of long energy-maximizing paths may be studied as a function of the paths’ pair of endpoint locations.
ALAN HAMMOND
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Forum of Mathematics, SigmaWe prove a new tableaux formula for the symmetric Macdonald polynomials $P_{\lambda }(X;q,t)$ that has considerably fewer terms and simpler weights than previously existing formulas. Our formula is a sum over certain sorted non-attacking tableaux,
Olya Mandelshtam
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Individual Based Model with Competition in Spatial Ecology
, 2009 . We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population in course of
Finkelshtein, Dmitri +5 more
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Forum of Mathematics, SigmaThe box-ball system (BBS), which was introduced by Takahashi and Satsuma in 1990, is a soliton cellular automaton. Its dynamics can be linearized by a few methods, among which the best known is the Kerov–Kirillov–Reschetikhin (KKR) bijection using rigged
Matteo Mucciconi +3 more
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Subcritical contact processes seen from a typical infected site
, 2020 What is the long-time behavior of the law of a contact process started with a single infected site, distributed according to counting measure on the lattice?
Jan M Swart, Anja Sturm
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Scaling limit of soliton lengths in a multicolor box-ball system
Forum of Mathematics, SigmaThe box-ball systems are integrable cellular automata whose long-time behavior is characterized by soliton solutions, with rich connections to other integrable systems such as the Korteweg-de Vries equation.
Joel Lewis +3 more
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