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Multivariate Ranks and Quantiles using Optimal Transportation and Applications to Goodness-of-fit Testing
A Glivenko-Cantelli type theorem is proved that shows the asymptotic stability of the empirical rank map in any direction, and proposes multivariate (nonparametric) goodness-of-fit tests based on the notion of quantiles and ranks.
Lower tail of the KPZ equation
We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data. Our bounds hold for all sufficiently large times $T$…
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables $X$ and $Y$ taking values in general topological spaces.…
Joint estimation of parameters in Ising model
We study joint estimation of the inverse temperature and magnetization parameters $(\beta,B)$ of an Ising model with a non-negative coupling matrix $A_n$ of size $n\times n$, given one sample from…
Stochastic PDE Limit of the Six Vertex Model
- Ivan Corwin, Promit Ghosal, Hao Shen, Li-Cheng Tsai
- MathematicsCommunications in Mathematical Physics
- 21 March 2018
We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $$\Delta \rightarrow 1^+$$ Δ → 1 + so as to zoom into the ferroelectric/disordered phase…
Entropic Optimal Transport: Geometry and Large Deviations
We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a…
Lyapunov exponents of the SHE for general initial data
We consider the $(1+1)$-dimensional stochastic heat equation (SHE) with multiplicative white noise and the Cole-Hopf solution of the Kardar-Parisi-Zhang (KPZ) equation. We show an exact way of…
Coulomb-Gas Electrostatics Controls Large Fluctuations of the Kardar-Parisi-Zhang Equation.
- Ivan Corwin, Promit Ghosal, Alexandre Krajenbrink, P. le Doussal, Li-Cheng Tsai
- MathematicsPhysical review letters
- 15 March 2018
A large deviation principle is established for the Kardar-Parisi-Zhang (KPZ) equation, providing precise control over the left tail of the height distribution for narrow wedge initial condition and rigorous proof of finite-time tail bounds on the KPZ distribution is provided.
Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections
Optimal transport maps between two probability distributions μ and ν on R have found extensive applications in both machine learning and statistics. In practice, these maps need to be estimated from…
KPZ equation tails for general initial data
- Ivan Corwin, Promit Ghosal
- Mathematics, Computer ScienceElectronic Journal of Probability
- 16 October 2018
The upper and lower tail probabilities for the centered and scaled one-point distribution of the Cole-Hopf solution of the KPZ equation when started with initial data drawn from a very general class are considered.