We prove that Schütz's ASEP Markov duality functional is also a Markov duality functional for the stochastic six vertex model. We introduce a new method that uses induction on the number of particles to prove the Markov duality.

A. We consider the n-point, fixed-time large deviations of the KPZ equation with the narrow wedge initial condition. The scope consists of concave-configured, upper-tail deviations and a wide range of scaling regimes that allows time to be short, unit-order, and long. We prove the n-point large deviation principle and characterize, with proof, the corresponding spacetime limit shape. Our proof is based on the results -from the companion paper [Tsa23] -on moments of the stochastic heat equation and utilizes ideas coming from a tree decomposition. Behind our proof lies the phenomenon where the major contribution of the noise concentrates around certain corridors in spacetime, and we explicitly describe the corridors.

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We consider the stochastic higher spin six vertex (SHS6V) model introduced by Corwin and Petrov [CP16] with general integer spin parameters I, J. Starting from near stationary initial condition, we prove that the SHS6V model converges to the Kardar-Parisi-Zhang (KPZ) equation under weakly asymmetric scaling. This generalizes the result in [CGST18, Theorem 1.1] from I = J = 1 to general I, J.

Brake-by-wire (BBW) system is the key system to ensure the safety and stability control of intelligent vehicle chassis. How to evaluate the BBW systems to meet the safety design requirements is one of the important links of system design. This article takes the BBW system as an example to illustrate the basic process of the safety assessment of intelligent vehicle. The fault tree analysis (FTA) method is used to quantitatively evaluate the failure status of the complete loss of the main brake function, and the fault tree analysis process is detailed. The results show that FTA plays an important role in guiding the design of system architecture. With the help of the importance index, we can quickly find out the weaknesses in the system architecture, when the probability of the failure state of the automobile brake-by-wire system cannot meet the ASIL requirements. Furthermore, effective countermeasures can be taken to optimize the design of the system architecture. Finally, the failure probability corresponding to the failure state of the car’s brake-by-wire system is reduced to 7×10-14.