Patrik L. Ferrari
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Patrik L. Ferrari has a total of 60 co-authors. Here are the top co-authors by number of shared publications:
- Herbert Spohn
Departments of Mathematics and Physics, Technical University of Munich, 85747 Garching, Germany
21 shared publications - Michael Praehofer
TU München
12 shared publications - Alexei Borodin
Massachusetts Institute of Technology
11 shared publications - Tomohiro Sasamoto
Mathematics Department Chiba University Yayoi-cho 1-33 263-8522 Inage Chiba Japan
10 shared publications - Alexei Borodin
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139
9 shared publications - Alessandra Occelli
Institute for Applied Mathematics Bonn University Endenicher Allee 60 53115 Bonn Germany
7 shared publications
Latest Publications
- Open Access
- 28 July 2026
- Published by Springer Nature in Mathematical Physics, Analysis and Geometry
- Vol. 29 (3) , 39
Decoupling and Decay of Two-Point Functions in a Two-Species (T)ASEP
We consider the two-species totally asymmetric simple exclusion process on $$\mathbb {Z}$$ with a translation-invariant stationary measure as the initial condition. We establish the asymptotic decoupling of the marginal height profiles along characteristic lines and prove the decay of the two-point functions in the large-time limit, thus confirming predictions of the nonlinear fluctuating hydrodynamics theory. Our approach builds on the queueing construction of the stationary measure introduced in [7, 32] and extends the theory of backwards paths for height functions developed in [14, 35]. The arguments for asymptotic decoupling also apply to further homogeneous initial data, and the decay of the two-point functions is proven for the stationary two-species asymmetric simple exclusion process, beyond the totally asymmetric case.- 28 July 2026
- Published by Springer Nature in Mathematical Physics, Analysis and Geometry
- Vol. 29 (3) , 39
Open AccessDecoupling and Decay of Two-Point Functions in a Two-Species (T)ASEP
We consider the two-species totally asymmetric simple exclusion process on $$\mathbb {Z}$$ with a translation-invariant stationary measure as the initial condition. We establish the asymptotic decoupling of the marginal height profiles along characteristic lines and prove the decay of the two-point functions in the large-time limit, thus confirming predictions of the nonlinear fluctuating hydrodynamics theory. Our approach builds on the queueing construction of the stationary measure introduced in [7, 32] and extends the theory of backwards paths for height functions developed in [14, 35]. The arguments for asymptotic decoupling also apply to further homogeneous initial data, and the decay of the two-point functions is proven for the stationary two-species asymmetric simple exclusion process, beyond the totally asymmetric case. - 1 February 2026
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 36 (1) , 451-493
Tagged particle fluctuations for TASEP with dynamics restricted by a moving wall
We consider the totally asymmetric simple exclusion process on Z with step initial condition and with the presence of a rightward-moving wall that prevents the particles from jumping. This model was first studied in (Ann. Inst. Henri Poincaré Probab. Stat. 60 (2024) 692–720). We extend their work by determining the limiting distribution of a tagged particle in the case where the wall has influence on its fluctuations in neighbourhoods of multiple macroscopic times.
- 1 February 2026
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 36 (1) , 451-493
Tagged particle fluctuations for TASEP with dynamics restricted by a moving wall
We consider the totally asymmetric simple exclusion process on Z with step initial condition and with the presence of a rightward-moving wall that prevents the particles from jumping. This model was first studied in (Ann. Inst. Henri Poincaré Probab. Stat. 60 (2024) 692–720). We extend their work by determining the limiting distribution of a tagged particle in the case where the wall has influence on its fluctuations in neighbourhoods of multiple macroscopic times.
- Open Access
- 11 August 2025
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 192 (8) , 1-33
Quasi-Geodesics in Integrable and Non-Integrable Exclusion Processes
Backwards geodesics for TASEP were introduced in [30]. We consider flat initial conditions and show that under proper scaling the end-point of the geodesic converges to maximizer argument of the $$\hbox {Airy}_2$$ process minus a parabola. We generalize its definition to generic non-integrable models including ASEP and speed changed ASEP (call it quasi-geodesics). We numerically verify that its end-point is universal, where the scaling coefficients are analytically computed through the KPZ scaling theory.- 11 August 2025
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 192 (8) , 1-33
Open AccessQuasi-Geodesics in Integrable and Non-Integrable Exclusion Processes
Backwards geodesics for TASEP were introduced in [30]. We consider flat initial conditions and show that under proper scaling the end-point of the geodesic converges to maximizer argument of the $$\hbox {Airy}_2$$ process minus a parabola. We generalize its definition to generic non-integrable models including ASEP and speed changed ASEP (call it quasi-geodesics). We numerically verify that its end-point is universal, where the scaling coefficients are analytically computed through the KPZ scaling theory. - 6 March 2025
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 134 (9) , 097104
Partial Yet Definite Emergence of the Kardar-Parisi-Zhang Class in Isotropic Spin Chains
Integrable spin chains with a continuous non-Abelian symmetry, such as the one-dimensional isotropic Heisenberg model, show superdiffusive transport with little theoretical understanding. Although recent studies reported a surprising connection to the Kardar-Parisi-Zhang (KPZ) universality class in that case, this view was most recently questioned by discrepancies in full counting statistics. Here, by combining extensive numerical simulations of classical and quantum integrable isotropic spin chains with a framework developed by exact studies of the KPZ class, we characterize various two-point quantities that remain hitherto unexplored in spin chains, and find full agreement with KPZ scaling laws without adjustable parameters. This establishes the partial emergence of the KPZ class in integrable isotropic spin chains. Moreover, we reveal that the KPZ scaling laws are intact in the presence of an energy current, under the appropriate Galilean boost required by the propagation of spacetime correlation.
- 6 March 2025
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 134 (9) , 097104
Partial Yet Definite Emergence of the Kardar-Parisi-Zhang Class in Isotropic Spin Chains
Integrable spin chains with a continuous non-Abelian symmetry, such as the one-dimensional isotropic Heisenberg model, show superdiffusive transport with little theoretical understanding. Although recent studies reported a surprising connection to the Kardar-Parisi-Zhang (KPZ) universality class in that case, this view was most recently questioned by discrepancies in full counting statistics. Here, by combining extensive numerical simulations of classical and quantum integrable isotropic spin chains with a framework developed by exact studies of the KPZ class, we characterize various two-point quantities that remain hitherto unexplored in spin chains, and find full agreement with KPZ scaling laws without adjustable parameters. This establishes the partial emergence of the KPZ class in integrable isotropic spin chains. Moreover, we reveal that the KPZ scaling laws are intact in the presence of an energy current, under the appropriate Galilean boost required by the propagation of spacetime correlation.
- Open Access
Mixing times for the open ASEP at the triple point
We consider mixing times for the open asymmetric simple exclusion process (ASEP) at the triple point. We show that the mixing time of the open ASEP on a segment of length $N$ for bias parameter $q$ is of order $N^{3/2+κ}$ if $1-q \asymp N^{-κ}$ for some $κ\in [0,\frac{1}{2})$, and the same result with poly-logarithmic corrections for $κ=\frac{1}{2}$. Our proof combines a fine analysis of the current of the open ASEP, moderate deviations of second class particles, the censoring inequality, and various couplings and multi-species extensions of the ASEP. Moreover, we establish a comparison between moderate deviations for the current of the open ASEP and the ASEP on the integers, as well as bounds on mixing times for the open ASEP in the weakly high density phase, which are of independent interest.Open AccessMixing times for the open ASEP at the triple point
We consider mixing times for the open asymmetric simple exclusion process (ASEP) at the triple point. We show that the mixing time of the open ASEP on a segment of length $N$ for bias parameter $q$ is of order $N^{3/2+κ}$ if $1-q \asymp N^{-κ}$ for some $κ\in [0,\frac{1}{2})$, and the same result with poly-logarithmic corrections for $κ=\frac{1}{2}$. Our proof combines a fine analysis of the current of the open ASEP, moderate deviations of second class particles, the censoring inequality, and various couplings and multi-species extensions of the ASEP. Moreover, we establish a comparison between moderate deviations for the current of the open ASEP and the ASEP on the integers, as well as bounds on mixing times for the open ASEP in the weakly high density phase, which are of independent interest. - Open Access
Quasi-geodesics in integrable and non-integrable exclusion processes
Backwards geodesics for TASEP were introduced in [Fer18]. We consider flat initial conditions and show that under proper scaling its end-point converges to maximizer argument of the Airy$_2$ process minus a parabola. We generalize its definition to generic non-integrable models including ASEP and speed changed ASEP (call it quasi-geodesics). We numerically verify that its end-point is universal, where the scaling coefficients are analytically computed through the KPZ scaling theory.
Open AccessQuasi-geodesics in integrable and non-integrable exclusion processes
Backwards geodesics for TASEP were introduced in [Fer18]. We consider flat initial conditions and show that under proper scaling its end-point converges to maximizer argument of the Airy$_2$ process minus a parabola. We generalize its definition to generic non-integrable models including ASEP and speed changed ASEP (call it quasi-geodesics). We numerically verify that its end-point is universal, where the scaling coefficients are analytically computed through the KPZ scaling theory.
- Open Access
The second class particle process at shocks
We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities $λ$ to the left of the origin and $ρ$ to the right of it and $λ<ρ$. We find an exact identity for the distribution of a second class particle starting at the origin. Then we determine the limiting joint distributions of the second class particle. Bypassing the last passage percolation model, we work directly in TASEP, allowing us to extend previous one-point distribution results via a more direct and shorter ansatz.Open AccessThe second class particle process at shocks
We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities $λ$ to the left of the origin and $ρ$ to the right of it and $λ<ρ$. We find an exact identity for the distribution of a second class particle starting at the origin. Then we determine the limiting joint distributions of the second class particle. Bypassing the last passage percolation model, we work directly in TASEP, allowing us to extend previous one-point distribution results via a more direct and shorter ansatz. - Open Access
- 1 January 2024
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 29 (none) , 1-44
Exact decay of the persistence probability in the Airy1 process
We consider the Airy1 process, which is the limit process in KPZ growth models with flat and non-random initial conditions. We study the persistence probability, namely the probability that the process stays below a given threshold c for a time span of length L. This is expected to decay as e−κ(c)L. We determine an analytic expression for κ(c) for all c≥3∕2 starting with the continuum statistics formula for the persistence probability. As the formula is analytic only for c>0, we determine an analytic continuation of κ(c) and numerically verify the validity for c<0 as well.
- 1 January 2024
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 29 (none) , 1-44
Open AccessExact decay of the persistence probability in the Airy1 process
We consider the Airy1 process, which is the limit process in KPZ growth models with flat and non-random initial conditions. We study the persistence probability, namely the probability that the process stays below a given threshold c for a time span of length L. This is expected to decay as e−κ(c)L. We determine an analytic expression for κ(c) for all c≥3∕2 starting with the continuum statistics formula for the persistence probability. As the formula is analytic only for c>0, we determine an analytic continuation of κ(c) and numerically verify the validity for c<0 as well.
- 6 January 2023
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 56 (1) , 014003
The Airy2 process and the 3D Ising model
The Ferrari–Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider M such diffusions conditioned not to intersect. We show that the top process converges to the Airy2 process as M → ∞ . We then explain the relation with the 3D Ising model and present some conjectures about it.
- 6 January 2023
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 56 (1) , 014003
The Airy2 process and the 3D Ising model
The Ferrari–Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider M such diffusions conditioned not to intersect. We show that the top process converges to the Airy2 process as M → ∞ . We then explain the relation with the 3D Ising model and present some conjectures about it.
- Open Access
The Airy$_2$ process and the 3D Ising model
The Ferrari-Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider $M$ such diffusions conditioned not to intersect. We show that the top process converges to the Airy$_2$ process as $M\to\infty$. We then explain the relation with the 3D Ising model and present some conjectures about it.Open AccessThe Airy$_2$ process and the 3D Ising model
The Ferrari-Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider $M$ such diffusions conditioned not to intersect. We show that the top process converges to the Airy$_2$ process as $M\to\infty$. We then explain the relation with the 3D Ising model and present some conjectures about it.