174 citations · 821 across the 30 of their papers we have counts for
27 papers · 1 filter
Exact solution of TASEP and variants with inhomogeneous speeds and memory lengths
Konstantin Matetski, Daniel Remenik
In [arXiv:1701.00018, arXiv:2107.07984] an explicit biorthogonalization method was developed that applies to a class of determinantal measures which describe the evolution of sever…
Polynuclear growth and the Toda lattice
Konstantin Matetski, Jeremy Quastel, Daniel Remenik
It is shown that the polynuclear growth model is a completely integrable Markov process in the sense that its transition probabilities are given by Fredholm determinants of kernels…
Integrable fluctuations in the KPZ universality class
Daniel Remenik
The KPZ fixed point is a scaling invariant Markov process which arises as the universal scaling limit of a broad class of models of random interface growth in one dimension, the on…
TASEP and generalizations: Method for exact solution
Konstantin Matetski, Daniel Remenik
The explicit biorthogonalization method, developed in [arXiv:1701.00018] for continuous time TASEP, is generalized to a broad class of determinantal measures which describe the evo…
Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
Karl Liechty, Gia Bao Nguyen, Daniel Remenik
We study the distribution of the supremum of the Airy process with wanderers minus a parabola, or equivalently the limit of the rescaled maximal height of a system of non-i…
One-sided reflected Brownian motions and the KPZ fixed point
Mihai Nica, Jeremy Quastel, Daniel Remenik
We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition pro…
KP governs random growth off a one dimensional substrate
Jeremy Quastel, Daniel Remenik
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) eq…
Solution of the Kolmogorov equation for TASEP
Mihai Nica, Jeremy Quastel, Daniel Remenik
We provide a direct and elementary proof that the formula obtained in [MQR17] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov back…
The contact process with dynamic edges on
Amitai Linker, Daniel Remenik
We study the contact process running in the one-dimensional lattice undergoing dynamical percolation, where edges open at rate and close at rate . Our goal is to explo…
Coexistence for a population model with forest fire epidemics
Luis Fredes, Amitai Linker, Daniel Remenik
We investigate the effect on survival and coexistence of introducing forest fire epidemics to a certain two-species competition model. The model is an extension of the one introduc…
The KPZ fixed point
Konstantin Matetski, Jeremy Quastel, Daniel Remenik
An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary…
Extreme statistics of non-intersecting Brownian paths
Gia Bao Nguyen, Daniel Remenik
We consider finite collections of non-intersecting Brownian paths on the line and on the half-line with both absorbing and reflecting boundary conditions (corresponding to Brow…
How flat is flat in random interface growth?
Jeremy Quastel, Daniel Remenik
Domains of attraction are identified for the universality classes of one-point asymptotic fluctuations for the Kardar-Parisi-Zhang (KPZ) equation with general initial data. The cri…
Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble
Gia Bao Nguyen, Daniel Remenik
We show that the squared maximal height of the top path among non-intersecting Brownian bridges starting and ending at the origin is distributed as the top eigenvalue of a rand…
A Pfaffian representation for flat ASEP
Janosch Ortmann, Jeremy Quastel, Daniel Remenik
We obtain a Fredholm Pfaffian formula for an appropriate generating function of the height function of the asymmetric simple exclusion process starting from flat (periodic) initial…
Exact formulas for random growth with half-flat initial data
Janosch Ortmann, Jeremy Quastel, Daniel Remenik
We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial…
Multiplicative functionals on ensembles of non-intersecting paths
Alexei Borodin, Ivan Corwin, Daniel Remenik
The purpose of this article is to develop a theory behind the occurrence of "path-integral" kernels in the study of extended determinantal point processes and non-intersecting line…
Airy processes and variational problems
Jeremy Quastel, Daniel Remenik
We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models.…
Tails of the endpoint distribution of directed polymers
Jeremy Quastel, Daniel Remenik
We prove that the random variable $\ct=\argmax_{t\in\rr}\{\aip(t)-t^2\}$ has tails which decay like . The distribution of $\ct$ is a universal distribution which governs…
Local behavior and hitting probabilities of the Airy1 process
Jeremy Quastel, Daniel Remenik
We obtain a formula for the -dimensional distributions of the Airy process in terms of a Fredholm determinant on $L^2(\rr)$, as opposed to the standard formula which involve…
Supremum of the Airy2 process minus a parabola on a half line
Jeremy Quastel, Daniel Remenik
Let $\aip(t)$ be the Airy process. We show that the random variable [\sup_{t\leqα}\{aip(t)-t^2}+\min{0,α}^2] has the same distribution as the one-point marginal of the Airy$_{2…
Endpoint distribution of directed polymers in 1+1 dimensions
Gregorio Moreno Flores, Jeremy Quastel, Daniel Remenik
We give an explicit formula for the joint density of the max and argmax of the Airy process minus a parabola. The argmax has a universal distribution which governs the rescaled…
Local Brownian property of the narrow wedge solution of the KPZ equation
Jeremy Quastel, Daniel Remenik
Let H(t,x) be the Hopf-Cole solution at time t of the Kardar-Parisi-Zhang (KPZ) equation starting with narrow wedge initial condition, i.e. the logarithm of the solution of the mul…
Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations
Rick Durrett, Daniel Remenik
We consider a branching-selection system in with particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, ke…