91 citations · 406 across the 28 of their papers we have counts for
35 papers
The Critical 2D KPZ Process
Quentin Berger, Francesco Caravenna, Jeremy Clark +8
This work constructs a non-trivial solution to the ill-defined two-dimensional Kardar-Parisi-Zhang (KPZ) equation at criticality: a distribution-valued stochastic process on the pl…
Fractional moments of the Stochastic Heat Flow and 2D Directed Polymers
Quentin Berger, Nicola Turchi, Nikos Zygouras
We estimate the fractional moments of the normalized mass assigned by the Critical 2D Stochastic Heat Flow to small balls. Our results also cover the discrete case corresponding to…
From disordered systems to the Critical 2D Stochastic Heat Flow
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
We review our joint work on the scaling limits of disordered systems, linking the notion of disorder relevance/irrelevance to that of sub/super-criticality of singular SPDEs. This…
Singularity and regularity of the critical 2D Stochastic Heat Flow
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
The Critical 2D Stochastic Heat Flow (SHF) provides a natural candidate solution to the ill-posed 2D Stochastic Heat Equation with multiplicative space-time white noise. In this pa…
The Critical 2d Stochastic Heat Flow and Related Models
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
In these lecture notes, we review recent progress in the study of the stochastic heat equation and its discrete analogue, the directed polymer model, in spatial dimension 2. It was…
On the moments of the mass of shrinking balls under the Critical Stochastic Heat Flow
Ziyang Liu, Nikos Zygouras
The Critical Stochastic Heat Flow (SHF) is a measure valued stochastic process on that defines a non-trivial solution to the two-dimensional stochastic heat equ…
Directed polymers in a random environment: a review of the phase transitions
Nikos Zygouras
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to comple…
The Allen-Cahn equation with weakly critical random initial datum
Simon Gabriel, Tommaso Rosati, Nikos Zygouras
This work considers the two-dimensional Allen-Cahn equation $$ \partial_t u = \frac{1}{2}Δu + \mathfrak{m}\, u -u^3\;, \quad u(0,x)= η(x)\;, \qquad \forall (t,x) \in [0, \infty) \t…
Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point
Elia Bisi, Yuchen Liao, Axel Saenz +1
We consider a discrete-time TASEP, where each particle jumps according to Bernoulli random variables with particle-dependent and time-inhomogeneous parameters. We use the combinato…
The critical 2d Stochastic Heat Flow is not a Gaussian Multiplicative Chaos
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
The critical Stochastic Heat Flow (SHF) is a stochastic process of random measures on , recently constructed in [CSZ23]. We show that this process falls outside…
A multivariate extension of the Erdös-Taylor theorem
Dimitris Lygkonis, Nikos Zygouras
The Erdös-Taylor theorem [Acta Math. Acad. Sci. Hungar, 1960] states that if is the local time at zero, up to time , of a two-dimensional simple, symmetric rando…
Moments of the 2d directed polymer in the subcritical regime and a generalisation of the Erdös-Taylor theorem
Dimitris Lygkonis, Nikos Zygouras
We compute the limit of the moments of the partition function of the directed polymer in dimension in the subcritical regime, i.e. when the inverse temperature…
The Critical 2d Stochastic Heat Flow
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
We consider directed polymers in random environment in the critical dimension , focusing on the intermediate disorder regime when the model undergoes a phase transition. We…
Edwards-Wilkinson fluctuations for the directed polymer in the full -regime for dimensions
Dimitris Lygkonis, Nikos Zygouras
We prove that in the full -regime the partition function of the directed polymer model in dimensions , if centered, scaled and averaged with respect to a test functio…
The geometric Burge correspondence and the partition function of polymer replicas
Elia Bisi, Neil O'Connell, Nikos Zygouras
We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation…
Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation
Elia Bisi, Nikos Zygouras
We study the combinatorial structure of the irreducible characters of the classical groups , , , ${\…
Some algebraic structures in KPZ universality
Nikos Zygouras
We review some algebraic and combinatorial structures that underlie models in the KPZ universality class.Emphasis is placed on the Robinson-Schensted-Knuth correspondence and its g…
The two-dimensional KPZ equation in the entire subcritical regime
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
We consider the KPZ equation in space dimension 2 driven by space-time white noise. We showed in previous work that if the noise is mollified in space on scale and its strength…
On the moments of the (2+1)-dimensional directed polymer and stochastic heat equation in the critical window
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
The partition function of the directed polymer model on Z^{2+1} undergoes a phase transition in a suitable continuum and weak disorder limit. In this paper, we focus on a window ar…
The Dickman subordinator, renewal theorems, and disordered systems
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
We consider the so-called Dickman subordinator, whose Levy measure has density 1/x restricted to the interval (0,1). The marginal density of this process, known as the Dickman func…
GOE and marginal distribution via symplectic Schur functions
Elia Bisi, Nikos Zygouras
We derive Sasamoto's Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the process, original…
Point-to-line polymers and orthogonal Whittaker functions
Elia Bisi, Nikos Zygouras
We study a one dimensional directed polymer model in an inverse-gamma random environment, known as the log-gamma polymer, in three different geometries: point-to-line, point-to-hal…
Scaling limits of disordered systems and disorder relevance
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
We review recent works where we have shown that disorder relevance is closely related to the existence of non-trivial, random continuum limits
Universality in marginally relevant disordered systems
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
We consider disordered systems of directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimens…