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We study a series of one-dimensional discrete-time quantum-walk modelslabeled by half integers $j=1/2, 1, 3/2, ...$, introduced by Miyazaki {\it etal.}, each of which the walker's wave function has $2j+1$ components andhopping range at each time step is $2j$. In long-time limit the densityfunctions of pseudovelocity-distributions are generally given by superpositionof appropriately scaled Konno's density function. Since Konno's densityfunction has a finite open support and it diverges at the boundaries ofsupport, limit distribution of pseudovelocities in the $(2j+1)$-component modelcan have $2j+1$ pikes, when $2j+1$ is even. When $j$ becomes very large,however, we found that these pikes vanish and a universal and monotone convexstructure appears around the origin in limit distributions. We discuss apossible route from quantum walks to classical diffusion associated with the $j\to \infty$ limit.

Large Qudit Limit of One-dimensional Quantum Walks