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Creators/Authors contains: "Lin, Yier"

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  1. ; (, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques)
    We consider the variational problem associated with the Freidlin--Wentzell Large Deviation Principle of the Stochastic Heat Equation (SHE). The logarithm of the minimizer of the variational problem gives the most probable shape of the solution of the Kardar--Parisi--Zhang equation conditioned on achieving certain unlikely values. Taking the SHE with the delta initial condition and conditioning the value of its solution at the origin at a later time, under suitable scaling, we prove that the logarithm of the minimizer converges to an explicit function as we tune the value of the conditioning to 0. Our result confirms the physics prediction Kolokolov and Korshunov (2009), Meerson, Katzav, and Vilenkin (2016), Kamenev, Meerson, and Sasorov (2016). 
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    Free, publicly-accessible full text available May 1, 2026
  2. ; (, Communications in Mathematical Physics)
    We consider the n-point, fixed-time large deviations of the KPZ equation with the narrow wedge initial condition. The scope consists of concave-configured, upper-tail deviations and a wide range of scaling regimes that allows time to be short, unit-order, and long. We prove the n-point large deviation principle and characterize, with proof, the corresponding spacetime limit shape. Our proof is based on the results—from the companion paper (Tsai in High moments of the SHE in the clustering regimes, 2023)—on moments of the stochastic heat equation and utilizes ideas coming from a tree decomposition. Behind our proof lies the phenomenon where the major contribution of the noise concentrates around certain corridors in spacetime, and we explicitly describe the corridors. 
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    Free, publicly-accessible full text available May 1, 2026
  3. ; ; (, Probability Theory and Related Fields)
    In this paper, we consider the KPZ equation under the weak noise scaling. That is, we introduce a small parameter \sqrt{\varepsilon} in front of the noise and let \varepsilon \to 0. We prove that the one-point large deviation rate function has a \frac{3}{2} power law in the deep upper tail. Furthermore, by forcing the value of the KPZ equation at a point to be very large, we prove a limit shape of the KPZ equation as \varepsilon \to 0. This confirms the physics prediction in Kolokolov and Korshunov (2007), Kolokolov and Korshunov (2009), Meerson, Katzav, and Vilenkin (2016), Kamenev, Meerson, and Sasorov (2016), and Le Doussal, Majumdar, Rosso, and Schehr (2016). 
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  4. ; (, Communications in mathematical physics)
    We establish the Freidlin–Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation with multiplicative noise in one spatial dimension. That is, we introduce a small parameter ε√ to the noise, and establish an LDP for the trajectory of the solution. Such a Freidlin–Wentzell LDP gives the short-time, one-point LDP for the KPZ equation in terms of a variational problem. Analyzing this variational problem under the narrow wedge initial data, we prove a quadratic law for the near-center tail and a 52 law for the deep lower tail. These power laws confirm existing physics predictions (Kolokolov and Korshunov in Phys Rev B 75(14):140201, 2007, Phys Rev E 80(3):031107, 2009; Meerson et al. in Phys Rev Lett 116(7):070601, 2016; Le Doussal et al. in Phys Rev Lett 117(7):070403, 2016; Kamenev et al. in Phys Rev E 94(3):032108, 2016). 
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  5. ; (, Communications in Mathematical Physics)
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  6. (, Mathematical Physics, Analysis and Geometry)
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  7. (, Electronic Journal of Probability)
    null (Ed.)
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