The maximum measured or theorized particle velocity in our current understanding of physics is the speed of light in vacuum, denoted by the symbol 'c'. According to the theory of special relativity, no particle with mass can reach or exceed the speed of light. The speed of light is approximately 299,792,458 meters per second.
Particles with zero rest mass, such as photons (particles of light), can travel at the speed of light. Photons, being massless, always move at this maximum velocity.
Regarding the concept of wave-particle duality, it is a fundamental principle in quantum mechanics that particles, including those with mass, can exhibit both particle-like and wave-like properties. This duality is not dependent on the particle's mass or velocity. It is a feature inherent to quantum objects, and the extent of their wave-like or particle-like behavior depends on the experimental setup and the nature of the observation being made.
In summary, particles with mass cannot travel faster than the speed of light, and the wave-particle duality applies to particles irrespective of their mass or velocity.