Shuta Nakajima
YOU?
Author Swipe
View article: Equivalence of fluctuations of discretized SHE and KPZ equations in the subcritical weak disorder regime
Equivalence of fluctuations of discretized SHE and KPZ equations in the subcritical weak disorder regime Open
We study the fluctuations of discretized versions of the stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation in spatial dimensions $d\geq 3$ in the weak disorder regime. The discretization is defined using the directe…
View article: Moderate deviations in first-passage percolation for bounded weights
Moderate deviations in first-passage percolation for bounded weights Open
We investigate the moderate and large deviations in first-passage percolation (FPP) with bounded weights on $\mathbb{Z}^d$ for $d \geq 2$. Write $T(\mathbf{x}, \mathbf{y})$ for the first-passage time and denote by $μ(\mathbf{u})$ the time …
View article: Lipschitz-type estimate for the frog model with Bernoulli initial configuration
Lipschitz-type estimate for the frog model with Bernoulli initial configuration Open
We consider the frog model with Bernoulli initial configuration, which is an interacting particle system on the multidimensional lattice consisting of two states of particles: active and sleeping. Active particles perform independent simpl…
View article: Lipschitz-continuity of time constant in generalized First-passage percolation
Lipschitz-continuity of time constant in generalized First-passage percolation Open
In this article, we consider a generalized First-passage percolation model, where each edge in $\mathbb{Z}^d$ is independently assigned an infinite weight with probability $1-p$, and a random finite weight otherwise. The existence and posi…
View article: Upper tail large deviation for the one-dimensional frog model
Upper tail large deviation for the one-dimensional frog model Open
In this paper, we study the upper tail large deviation for the one-dimensional frog model. In this model, sleeping and active frogs are assigned to vertices on $\mathbb Z$. While sleeping frogs do not move, the active ones move as independ…
View article: Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor
Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor Open
A quantum kicked rotor model is one of the promising systems to realize various Floquet topological phases. We consider a double-kicked rotor model for a one-dimensional quasi-spin-1/2 Bose-Einstein condensate with spin-dependent and spin-…
View article: Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor
Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor Open
A quantum kicked rotor model is one of the promising systems to realize various Floquet topological phases. We consider a double-kicked rotor model for a one-dimensional quasi-spin-1/2 Bose-Einstein condensate with spin-dependent and spin-…
View article: Injectivity of ReLU networks: perspectives from statistical physics
Injectivity of ReLU networks: perspectives from statistical physics Open
When can the input of a ReLU neural network be inferred from its output? In other words, when is the network injective? We consider a single layer, $x \mapsto \mathrm{ReLU}(Wx)$, with a random Gaussian $m \times n$ matrix $W$, in a high-di…
View article: Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions
Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions Open
The solution of Kardar-Parisi-Zhang equation (KPZ equation) is solved formally via Cole-Hopf transformation $h=\log u$, where $u$ is the solution of multiplicative stochastic heat equation(SHE). In earlier works by Chatterjee and Dunlap, C…
View article: On the upper tail large deviation rate function for chemical distance in supercritical percolation
On the upper tail large deviation rate function for chemical distance in supercritical percolation Open
We consider the supercritical bond percolation on $\mathbb Z^d$ and study the graph distance on the percolation graph called the chemical distance. It is well-known that there exists a deterministic constant $μ(x)$ such that the chemical d…
View article: Sharp threshold sequence and universality for Ising perceptron models
Sharp threshold sequence and universality for Ising perceptron models Open
We study a family of Ising perceptron models with $\{0,1\}$-valued activation functions. This includes the classical half-space models, as well as some of the symmetric models considered in recent works. For each of these models we show th…
View article: Maximal edge-traversal time in First-passage percolation
Maximal edge-traversal time in First-passage percolation Open
In this paper, we study the maximal edge-traversal time on optimal paths in First-passage percolation on the lattice Zd for several edge distributions, including the Pareto and Weibull distributions. It is known to be unbounded when the ed…
View article: Asymptotics of the $p$-capacity in the critical regime
Asymptotics of the $p$-capacity in the critical regime Open
In this note, we are interested in the asymptotics as $n\to\infty$ of the $p$-capacity between the origin and the set $nB$, where $B$ is the boundary of the unit ball of the lattice $\mathbb Z^d$. The $p$-capacity is defined as the minimum…
View article: Gardner formula for Ising perceptron models at small densities
Gardner formula for Ising perceptron models at small densities Open
We consider the Ising perceptron model with N spins and M = N*alpha patterns, with a general activation function U that is bounded above. For U bounded away from zero, or U a one-sided threshold function, it was shown by Talagrand (2000, 2…
View article: A variational formula for large deviations in First-passage percolation under tail estimates
A variational formula for large deviations in First-passage percolation under tail estimates Open
Consider first passage percolation with identical and independent weight distributions and first passage time ${\rm T}$. In this paper, we study the upper tail large deviations $\mathbb{P}({\rm T}(0,nx)>n(μ+ξ))$, for $ξ>0$ and $x\neq 0$ wi…
View article: Law of large numbers and fluctuations in the sub-critical and $L^2$ regions for SHE and KPZ equation in dimension $d\geq 3$
Law of large numbers and fluctuations in the sub-critical and $L^2$ regions for SHE and KPZ equation in dimension $d\geq 3$ Open
There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension $d\geq 3$ as the smoothing parameter is switched off, but most of the results did not hold i…
View article: Law of large numbers and fluctuations in the sub-critical and $L^2$\n regions for SHE and KPZ equation in dimension $d\\geq 3$
Law of large numbers and fluctuations in the sub-critical and $L^2$\n regions for SHE and KPZ equation in dimension $d\\geq 3$ Open
There have been recently several works studying the regularized stochastic\nheat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension $d\\geq\n3$ as the smoothing parameter is switched off, but most of the results did not\nho…
View article: Divergence of non-random fluctuation for Euclidean first-passage percolation
Divergence of non-random fluctuation for Euclidean first-passage percolation Open
The non-random fluctuation is one of the central objects in first passage percolation. It was proved in [Shuta Nakajima. Divergence of non-random fluctuation in First Passage Percolation. {\em Electron. Commun. Probab.} 24 (65), 1-13. 2019…
View article: Upper tail large deviations for a class of distributions in First-passage percolation
Upper tail large deviations for a class of distributions in First-passage percolation Open
In this paper we consider the first passage percolation with identical and independent exponentially distributions, called the Eden growth model, and we study the upper tail large deviations for the first passage time ${\rm T}$. Our main r…
View article: Passage time of the frog model has a sublinear variance
Passage time of the frog model has a sublinear variance Open
In this paper, we show that the first passage time in the frog model on $\Z^d$ with $d\geq 2$ has a sublinear variance. This implies that the central limit theorem does not holds at least with the standard diffusive scaling. The proof is b…
View article: Dissipative Bose-Hubbard system with intrinsic two-body loss
Dissipative Bose-Hubbard system with intrinsic two-body loss Open
We report an experimental study of dynamics of the metastable $^3P_2$ state\nof bosonic ytterbium atoms in an optical lattice. The dissipative Bose-Hubbard\nsystem with on-site two-body atom loss is realized via its intrinsic strong\ninela…
View article: Gaussian fluctuations for the directed polymer partition function for $d\geq 3$ and in the whole $L^2$-region
Gaussian fluctuations for the directed polymer partition function for $d\geq 3$ and in the whole $L^2$-region Open
We consider the discrete directed polymer model with i.i.d. environment and we study the fluctuations of the tail $n^{(d-2)/4}(W_\infty - W_n)$ of the normalized partition function. It was proven by Comets and Liu, that for sufficiently hi…
View article: Passage time of the frog model has a sublinear variance
Passage time of the frog model has a sublinear variance Open
In this paper, we show that the passage time in the frog model on Z d with d ≥ 2 has a sublinear variance. The proof is based on the method introduced in [8] combining with tessellation arguments to estimate the martingale difference. We a…
View article: First passage time of the frog model has a sublinear variance
First passage time of the frog model has a sublinear variance Open
In this paper, we show that the first passage time in the frog model on $\\mathbb{Z} ^{d}$ with $d\\geq 2$ has a sublinear variance. This implies that the central limit theorem does not hold at least with the standard diffusive scaling. Th…
View article: Divergence of non-random fluctuation in First Passage Percolation
Divergence of non-random fluctuation in First Passage Percolation Open
We study the non-random fluctuation in first passage percolation and show that it diverges. We also prove the divergence of non-random shape fluctuation, which was predicted in [Yu Zhang. The divergence of fluctuations for shape in first p…
View article: Ergodicity of the number of infinite geodesics originating from zero
Ergodicity of the number of infinite geodesics originating from zero Open
First-passage percolation is a random growth model which has a metric structure. An infinite geodesic is an infinite sequence whose all sub-sequences are shortest paths. One of the important quantity is the number of infinite geodesics ori…
View article: Divergence of non-random fluctuation in First Passage Percolation
Divergence of non-random fluctuation in First Passage Percolation Open
We study non-random fluctuation in the first passage percolation on $\mathbb{Z}^d$ and show that it diverges for any dimension. We also prove the divergence of the non-random shape fluctuation, which was conjectured in [Yu Zhang. The diver…