Emergence of patterns in random processes.

Sixty years ago, it was observed that any independent and identically distributed (i.i.d.

Statistical properties of record-breaking temperatures.

A record-breaking temperature is the highest or lowest temperature at a station since the period of time considered began. The temperatures at a station constitute a time series. After the removal of daily and annual periodicities, the primary considerations are trends (i.

Characterizing wildfire regimes in the United States.

Wildfires statistics for the conterminous United States (U.S.) are examined in a spatially and temporally explicit manner.

Self-organization, the cascade model, and natural hazards.

We consider the frequency-size statistics of two natural hazards, forest fires and landslides. Both appear to satisfy power-law (fractal) distributions to a good approximation under a wide variety of conditions. Two simple cellular-automata models have been proposed as analogs for this observed behavior, the forest fire model for forest fires and the sand pile model for landslides.