Due to unbalanced distribution of tourists during peak time, tourists are likely to highly flock in certain areas of scenery spots if imperfect organization and management. For this reason, there may be crowds or even trample accidents in addition to unrecoverable damages for the ecological environment in such areas. Therefore, the valid solution is to formulate scientific tourist diversion str...

Let (Zn)n∈N0 be a d-dimensional random walk in random scenery, i.e., Zn = ∑n−1 k=0 YSk with (Sk)k∈N0 a random walk in Z d and (Yz)z∈Zd an i.i.d. scenery, independent of the walk. We assume that the random variables Yz have a stretched exponential tail. In particular, they do not possess exponential moments. We identify the speed and the rate of the logarithmic decay of P( 1 nZn > tn) for all se...

Let {ξ(n)}n∈Z be a two-color random scenery, that is, a random coloring of Z in two colors, such that the ξ(i)’s are i.i.d. Bernoulli variables with parameter 1 2 . Let {S(n)}n∈N be a symmetric random walk starting at 0. Our main result shows that a.s., ξ ◦ S (the composition of ξ and S) determines ξ up to translation and reflection. In other words, by observing the scenery ξ along the random w...

Generation and real-time rendering of terrain is a complex and multifaceted problem. Besides the obvious trade-offs between performance and quality, many different generation and rendering solutions exist. Different choices in implementation will result in very different visuals, usability and tools for generation. In this thesis, a fast and intuitive terrain generation method based on sketchin...