The Scaling Limit of the KPZ Equation in Space Dimension 3 and Higher
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DOI: 10.1007/s10955-018-2014-0
Abstract: We study in the present article the Kardar–Parisi–Zhang (KPZ) equation $$\begin{aligned} \partial _t h(t,x)=\nu \Delta h(t,x)+\lambda |\nabla h(t,x)|^2 +\sqrt{D}\, \eta (t,x), \qquad (t,x)\in \mathbb {R}_+\times \mathbb {R}^d \end{aligned}$$∂th(t,x)=νΔh(t,x)+λ|∇h(t,x)|2+Dη(t,x),(t,x)∈R+×Rdin $$d\ge 3$$d≥3 dimensions in the perturbative regime,… read more here.
Keywords: lambda; space; scaling limit; kpz equation ... See more keywords
High-Temperature Scaling Limit for Directed Polymers on a Hierarchical Lattice with Bond Disorder
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DOI: 10.1007/s10955-019-02241-3
Abstract: Diamond “lattices” are sequences of recursively-defined graphs that provide a network of directed pathways between two fixed root nodes, A and B. The construction recipe for diamond graphs depends on a branching number $$b\in {\mathbb… read more here.
Keywords: temperature; high temperature; limit; scaling limit ... See more keywords
Scaling limit theorem for transient random walk in random environment
Sign Up to like & getrecommendations! Published in 2018 at "Frontiers of Mathematics in China"
DOI: 10.1007/s11464-018-0723-y
Abstract: We construct a sequence of transient random walks in random environments and prove that by proper scaling, it converges to a diffusion process with drifted Brownian potential. To this end, we prove a counterpart of… read more here.
Keywords: transient random; random environment; scaling limit; random ... See more keywords
Confinement Effects on Radiation Response of SOI FinFETs at the Scaling Limit
Sign Up to like & getrecommendations! Published in 2017 at "IEEE Electron Device Letters"
DOI: 10.1109/led.2017.2661239
Abstract: This letter demonstrates the impact of carrier confinement on the radiation response of Si-based SOI finFETS toward the scaling limit. A comparison between the semi-classical and quantum (i.e., self-consistent Schrödinger–Poisson) calculations establishes the significance of… read more here.
Keywords: confinement; scaling limit; radiation response; soi finfets ... See more keywords
Hyperbolic scaling limit of non-equilibrium fluctuations for a weakly anharmonic chain
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DOI: 10.1214/20-ejp488
Abstract: We consider a chain of n coupled oscillators placed on a one-dimensional lattice with periodic boundary conditions. The interaction between particles is determined by a weakly anharmonic potential Vn = r 2 /2 + σnU… read more here.
Keywords: chain; hyperbolic scaling; limit non; weakly anharmonic ... See more keywords
Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense
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DOI: 10.1214/21-ejp659
Abstract: Recent works have shown that random triangulations decorated by critical ($p=1/2$) Bernoulli site percolation converge in the scaling limit to a $\sqrt{8/3}$-Liouville quantum gravity (LQG) surface (equivalently, a Brownian surface) decorated by SLE$_6$ in two… read more here.
Keywords: random triangulations; metric peanosphere; site percolation; percolation ... See more keywords
Scaling limit of a kinetic inhomogeneous stochastic system in the quadratic potential
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DOI: 10.3934/dcds.2023042
Abstract: We consider a particle evolving in the quadratic potential and subject to a time-inhomogeneous frictional force and to a random force. The couple of its velocity and position is solution to a stochastic differential equation… read more here.
Keywords: frictional force; scaling limit; force; quadratic potential ... See more keywords